Articular cartilage, which is composed with a solid phase of collagen fibers and proteoglycan and a pore fluid phase, can be depicted with two-phase porous medium model based on mixture theory. This paper analyzed the creep and stress relaxation responses of confined compression problems of articular cartilage with the developed finite element method. The obtained responses of velocities of both solid and fluid phases and the effective stresses of solid phase as well as the pore pressures during the creep and stress relaxation processes of articular cartilage tissues under confined compression can be used as a theoretical reference for man-made cartilage materials, and behave important significance for the research in bio-mechanical engineering area.