A model of articular cartilage is developed in which the continuum stiffness tensor is related to the tissue's microstructure. The model consists of bilinear elastic fibers embedded in an elastic matrix. Homogenization techniques are used to relate this level of organization to the macroscopic response of the tissue. The model includes the effects of spatial orientation of fibers, pre-stress in the fibers and matrix resulting from matrix swelling, slipping at the interface between the fibers and the matrix, fiber buckling in compression, and deformation-induced fiber reorientation. The model predicts increased axial stiffness with increasing stretch due to fiber reorientation, reduced axial and shear stiffness with slipping between fiber and matrix and a sensitivity of the tissue response to the swelling pressure in the matrix, the matrix modulus and the bonding of the fiber matrix interface.