The macromechanical tribological mechanism describes the friction phenomenon by considering the stress and the strain distributions, and the total elastic and plastic deformations. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (CPM). The Lagrange multiplier approach is adopted for imposing the inequality contact constraints. The Coulomb's friction law and the Prandtl–Reuss flow rule are used for the friction conditions and the elastoplastic behavior, respectively. The frictional contact examples are analyzed using the developed adaptive incremental procedure to elucidate the tribological behavior of the contact bodies and the model applicability.