The articular contact surfaces in human and animal joints are highly variable. Articular cartilage thickness and the material properties of the cartilage vary as a function of location in the joint and may also change in the pathologic state. In order to study practical joint contact problems, we extended the model for the contact of two biphasic cartilage layers proposed by Ateshian et al. [J. Biomechanics 27, 1347-1360 (1994)] by combining the assumption of the kinetic relationship from classical contact mechanics with the joint contact model for biphasic articular cartilage. In order to illustrate the characteristics of the proposed model, the contact problem was solved numerically for different curvatures of the contact surfaces, and for different thicknesses and material properties of the cartilage layers. Each cartilage layer was assumed to have constant thickness within the contact region. The contact radius, the relative displacement between the contacting bodies, contact pressure, and the stress distributions within the cartilage layers were calculated by applying a step load for a time period of 200 s. The contact radius was found to be sensitive to the change in thickness of the cartilage, and was not very sensitive to the change in the material property of the cartilage. The peak effective stress and the maximal shear stress were predicted to occur at the cartilage-bone interface for all simulated cases, which is in agreement with other theoretical research and supports the experimental findings in the literature on the origins of cartilage damage. For articular cartilage layers of different thicknesses, the stresses in the thick layer were found to be higher than those in the thin layer. Compared to other models of joint contact, the present model offers more possibilities for investigating practical applications, such as simulating the effects associated with cartilage degeneration in diseases such as osteoarthritis, and comparing theoretical predictions with experimental measurements of pressure distribution and contact area in joints.