Modigliani is known for his nudes. They are sexy. Art historians find this a problem. Some of Modigliani's models found this a problem, too. For different reasons. Not for moral reasons like the shiftiness of removing your shift for a shufti - you know, pornography, voyeurism, the male gaze - but for anatomical reasons. As I will explain.  In Tom Stoppard's radio play, In the Native State, a fictional young poet, Flora Crewe, has been a model for Modi - as she calls Modigliani. She is, shall we say, uninhibited. This is a sample of her racy poetry: "Sweat collects and holds as a pearl at my throat, / lets go and slides like a tongue-tip / down a Modigliani." There is a word understood here: "down a Modigliani [nude]". Thereafter the poem (and the tongue-tip) head southwards: "now in the salt-lick", "a seed pearl returning to the oyster". Her sister Eleanor offers a gloss on Flora's libidinous temperament: "Men were not really important to Flora. If they had been, they would have been fewer. She used them like batteries. When things went flat, she'd put in a new one."  Let Flora Crewe stand for the women in Modigliani's short, serried and, we hope, rank erotic life. Which included a poetic fling (1910-1911) with Anna Akhmatova, to whom he gave 16 portrait drawings - which were lost at Tsarskoye Selo during the first revolution: "The one that survived is less characteristic of his later nudes than the others," she confessed in Poem without a Hero.  She is seated nude in a wing-backed armchair, her head turned in profile to her left, resting on her shoulder. This tells you nothing. Her eye is closed. Her nose is faintly aquiline. She isn't tall so much as prolonged. And the lines of her slim torso go on endlessly. It inhabits a dark outline. Without the chair - which is five lines only, one broken - the nude would be nothing. The charm is the contrast between her angular curves and the slightly curved angles of the chair. She is more curved. The chair is more angular. But Modigliani hints at marriage - at squaring the circle. The angles have it.  After Akhmatova, there was a subsequent thing with the poet and writer Beatrice Hastings who had been a circus performer in the Transvaal. Then a final affair with the painter Jeanne Hébuterne, who committed suicide after Modigliani's death, aged 35, from alcohol and tuberculosis in 1920. There were probably others.  Akhmatova, with her 15 lost drawings, may have been Stoppard's model for the model and poet Flora Crewe - whose nude picture is bought by her jealous fiance and burned. In any case, Flora Crewe has penetrating things to say about Modigliani's nudes: "I had to lie with my shoulders flat but my hips twisted towards the canvas; I could hardly move afterwards."  This is what John Updike means when he says, in Just Looking, that Modigliani's Reclining Nude or Le Grand Nu in Moma is "anatomically impossible". To realise this, you turn the picture on its side so you can see la grande horizontale in the vertical. As viewers, we are mesmerised by the solid swell of the breasts - which begin at the collarbone, and are so big the woman isn't flat-chested even when lying on her back. (It looks impossible, but it is only rare.) And we are mesmerised by the waist extension - an extra foot, which is as impossible as it sounds - so that we don't notice the perfunctory hands.  Modigliani doesn't want us to notice the hands. They are finessed away as fatally finicky, a compositional complication. What we are offered is sexy, but a simplification. The pelvis - in a different plane from the upper body - is turned to the viewer to maximise the arc of the hips. The artist has turned his model like a Rubik's cube below the waist. If you are inclined to acquit the artist - from the charge of painting kitsch, of painting sexual fantasy, of beautifying the banal - you call this stylisation. You invoke the Willendorf Venus  I wonder whether Botticelli's Venus isn't a better parallel. All Modigliani's paintings have cubist-lite elements and classical Renaissance traits. (For instance, the visible under-paint, the glimpses of canvas are meant to evoke the fresco.) Botticelli's nudes are pleasing but anatomically implausible - he can't quite work out how the ankles join the feet. And his Venus in the Gemäldegalerie in Berlin has a left arm almost as long as her left leg - she needs it to gather her golden hair over her modesty. But we don't notice, because the eye is conventional and therefore compensates. Human beings interpret, they fudge, they are nostalgic for the normal. At an eclipse of the sun, the temperature drop is radical, dramatic - but our bodies tell us something different, they register a lesser change.  These Renaissance liberties with physiology give Modigliani the necessary licence to undertake his own alterations - to take in, to let out, to tailor his material. For instance, Reclining Female Nude 1917 has had her (compositionally troublesome) left arm amputated and her pelvis exaggerated - or her waist taken in. The trouble is that Modigliani's nudes tend to the formulaic. Ever seen a Modigliani nude with a dumpy waist? No, of course not. Is this repetition? Or is it perfectionism? Or is it a style?  But just as one inclines to a negative verdict, one remembers Brancusi - an infinitely greater artist than Modigliani, a radical artist whose ideas Modigliani borrowed and popularised. But Brancusi made (at a rough count) 21 Birds in Space, in a variety of materials - bronze, marble, plaster. I think I saw 13 on show at the Centre Pompidou, Paris, in 1995, and marvelled at the crucial, infinitesimal differences that meant only two of the 13 achieved the weightlessness sought by the sculptor. There are also 12 Fish by Brancusi and at least 16 Sleeping Muses ... No one thinks Brancusi limited or formulaic.  Brancusi was, we tend to forget, a great portraitist - both in his early, conventional sculptures and, on occasion, in his drawings. Think of his great drawing of Joyce - specs, tache - a schoolboy's maladroit simplification of genius. And Modigliani's portraits deserve to be as famous as his nudes. Of course, like the nudes, they over-insist on their stylistic signatures - the blank black asymmetric eyes out of Cézanne and (say) Picasso's 1906 Portrait of Gertrude Stein. The empty eye matched with a "conventional" dark eye is also indebted to Picasso - for example, his study for Les Demoiselles d'Avignon (1907) in the National Museum for Modern Art in Paris. Don't get me started on his nose-jobs - those wedges out of Africa and Picasso. Not exactly forgeries, but forged originally in someone else's foundry - where they were "found" by Modigliani.  I'd like to look at Modigliani's portraits of his quondam mistress Beatrice Hastings, the Jewish poet Max Jacob, Cocteau, the sculptor Lipchitz and the painter Diego Rivera. Photographs of all these sitters survive. They show us that Modigliani had a gift for likeness, which he sometimes, rightly, chose to override - in the interest of inspired equivalence. Brancusi's portrait of Joyce is the perfect example of inspired equivalence - a facial kit, a sketch, a gathering together of the ingredients for a portrait. In Modigliani, there is nothing so radical, but there is a negotiation between likeness and stylistic features. His best portraits are where the two poles are closest - the pictures of children, who are naturally simplified. Children are notoriously difficult to paint convincingly, their features disguised by the anonymity of innocence. Modigliani brings it off triumphantly.  Modigliani's technique of stylisation - its candid asymmetry, its shared cubist elements, its uneven eyes, the jigsaw fit of the nostrils to the outline of the upper lip - is to spike the mannerist touches with plausible and vivid realistic detail. Diego Rivera's eyes are two navels sunk in flesh, the plump fish lips are minimised by the fat moon face. His beard is a seethe of ants. There is an element of brilliant pudgy caricature. Rivera resembles his photograph, but he resembles (we think) Modigliani's painting more. Cocteau complained about his mouth. It is prissy, a rosebud - whereas in photographs it is lean and rather wide. Modigliani's portrait is painted out of homophobic distaste and drawing-room cubism. It is all poise and pose -close to caricature, then, libellous even, but true in the way that Picasso's 1905 portrait of Apollinaire as a pipe-sucking pomegranate is irrefutable.  Lipchitz hardly resembles his photograph at all. The trick, though, is the same. He is given a standard stylised nose out of stores, but his supplementary detail includes asymmetric hair, solid as a wig, an incipient prickle of sparse moustache (like a shaven armpit) and an incipient double chin, whose fold is mirrored in his polo neck.  There are approximately seven oils and two drawings of Beatrice Hastings - another possible model for Tom Stoppard's Flora Crewe. Her surviving photograph - of a woman in a waisted jacket with mutton-chop sleeves, an elaborate feathered hat and a tough-ish mouth - tells us very little. Modigliani's pencil drawings (circa 1915) tell us more - both about her face and the fleeting influence of chinoiserie. Two paintings record a Ronald Searle-like upturned nose in oil and pencil (1916), then the same nose repeated in oil, plus hooded cubist eyes, cheekbones she shares with the Max Jacob oil and a boldly rendered check dress taken from Matisse.  In 1916, there is yet another portrait of Beatrice in a high-collared overcoat - at the centre of overlapping planes is the same nose on the same trajectory, one eyebrow only, one blank eye and one black eye. The mouth looks tight - the mouth of a woman at the end of an affair, just ever so slightly pissed off. The picture is full of character. Subsequently, she is more stylised: her widely set eyes closer together, both of them black, the nose straight, seen frontally, the mouth tiny, hardly the width of her nostrils, the columnar neck a beanstalk. The pictures are full of character - of containment, of resignation, of realistic assessment. In approximately two years, Modigliani has exhausted her facial individuality and assimilated her to his style - miraculously without mislaying her likeness.  A last word about Max Jacob. According to Beatrice Hastings, Modigliani "despised everyone but Picasso and Max Jacob". She adds that he "loathed Cocteau". There are two Modigliani portraits of Jacob - one relatively conventional, one of Jacob in a top hat and a tie, whose checks are repeated in the sitter's left eye. It is the mouth that interests me. It is thin, a little pinched, but somehow benignly humorous, as if reflecting on and relishing a joke with a slow burn - the opposite of Cocteau. It bears out Beatrice Hastings's testimony.  Modigliani may not be a great painter - and his early death may have saved him from what Picasso called the "abject" fate of imitating himself even more than he does now, but what remains is charming, often sexy and unquestionably talented.  · Modigliani and His Models is at the Sackler Wing of Galleries at the Royal Academy, London W1, until October 15. Details: 020-7300 8000.
Modigliani may not have been a great painter, but he was a very stylish one. And there is more to his work than his wonderfully sexy, if anatomically impossible, nudes, argues Craig Raine.