The effect of three different friction interface models on an elastic half-space is presented. Three constitutive friction models are studied: Coulomb, soil–concrete interface, and Bouc–Wen, using a computational mechanics framework that can represent the contact patch's material response to static and dynamic surface tractions. This response is observed as strains and stresses present from reciprocating sliding using an elastoplastic friction (EPF) algorithm that also captures energy dissipation and hysteresis due to friction sliding. Additionally, the use of the four-parameter Bouc–Wen model represents a new development in contact mechanics that allows micro-slip of the contact interface to be modeled. Hysteresis loops are generated for the three friction models based on a quasi-static assumption. This algorithm is built into a mesoscale finite element method solver that is able to simulate different loading conditions and provide insight into how the friction models respond to load conditions and inform on experimental data. The energy dissipation from reciprocating friction sliding will be generated for each friction model as a metric that captures surface wear and potential material damage.