A finite element model of the meniscus is presented, based on an axisymmetric geometric approximation of the menisci and a biphasic description of the tissue as a mixture of solid and fluid components. The highly fibrous nature of the meniscal tissue is accounted for by using a fiber-reinforced, transversely isotropic description of the solid phase. This model is used to study the response of a meniscus resting on a perfectly lubricated tibial surface and subjected to distributed loads applied to the femoral surface, and to examine the effects of changes in loading conditions at the femoral and tibial interfaces. Quantities of interest include the stress, pressure and strain distributions at discrete times early in the meniscal response, and the flow of the fluid phase relative to the solid phase. Of particular interest are regions of large tensile strains which could lead to meniscal failures such as the bucket-handle tear. We show that all components of strain are positive in regions of the outer third of the meniscus, and that the maximum tensile strain perpendicular to the circumferentially arranged fibers (largest principal strain in the axisymmetric cross section) is positive throughout most of the cross section. Changing the partition of the load on the femoral surface and the permeability at the tibial surface changes the time-dependent response, but has little effect on the strain distributions at times of the order of 5 s considered in this study. The inclusion of a transversely isotropic, fibrous representation of the solid phases is shown to be essential to proper meniscal simulation. The results demonstrate the importance of the biphasic representation since the fluid phase is shown to carry a significant part of the applied load.