In this work, we developed a finite element modeling approach to study adhesion during unidirectional contact between a two-dimensional plane-strain square and a flat slab. The surfaces were metallic or ceramic, and we analyzed different pairs of materials and their adhesion intensity using a FORTRAN subroutine (DLOAD) connected to a commercial finite element code Abaqus, which provided the surface attractive forces based on the Lennard-Jones interatomic potential using Hamaker constants. We considered adhesive loads during both the approach and separation of the surfaces. During the separation step, we modeled the material transfer between surfaces due to adhesion with respect to damage initiation and propagation at the flat slab. The parameters considered in the simulations include normal load, chemical affinity, and system size, and we analyzed different conditions by comparing the interaction forces during approach and withdrawal. This work also presents: (i) a description of the evolution of energy dissipation due to adhesion hysteresis, (ii) the formation–growth–breakage process of the adhesive junctions and the material transfer between surfaces, and (iii) an adhesive wear map based on a proposed novel equation that correlates the material parameters and material loss due to adhesion. The results indicate that the chemical affinity between bodies in contact is more related to adhesion than the applied load. In addition, the ratio between the material strength and elastic modulus seems to be an important factor in reducing adhesive wear.