Moving contact is fundamental to understanding the mechanical environment of articular cartilage in diarthrodial joints. This study presents a method for approximating three-dimensional (3D) moving contact of biphasic tissue layers using a time-dependent penetration method. This technique has been implemented in a custom finite element solution framework for large-scale simulation that includes a graphical user interface, automatic meshing, and visualization tools. Thus, physiological geometry and load levels can be simulated by this approximate technique. The method is illustrated for canonical and physiological problems representing the glenohumeral joint (GHJ) of the shoulder.