A novel squeeze pressure bioreactor for noncontact hydrodynamic stimulation of cartilage is described. The bioreactor is based on a small piston that moves up and down, perpendicular to a tissue construct, in a fluid-filled chamber. Fluid displaced by the piston generates a pressure wave and shear stress as it moves across the sample, simulating the dynamic environment of a mobile joint. The fluid dynamics inside the squeeze pressure bioreactor was modeled using analytical and computational methods to simulate the mechanical stimuli imposed on a construct. In particular, the pressure, velocity field, and wall shear stress generated on the surface of the construct were analyzed using the theory of hydrodynamic lubrication, which describes the flow of an incompressible fluid between two surfaces in relative motion. Both the models and in-situ pressure measurements in the bioreactor demonstrate that controlled cyclic stresses of up to 10 kPa can be applied to tissue constructs. Initial tests on three-dimensional scaffolds seeded with chondrocytes show that glycosaminoglycan production is increased with regard to controls after 24 and 48 h of cyclic noncontact stimulation in the bioreactor.