A model for the mild wear of two contacting solids and an analytical example are proposed in this article. The model includes the presence of an interface made of damaged materials, fluid and wear debris. It consists in a wear criterion, an interface law and complementary relations deduced from the mass conservation. A thermodynamical analysis provides energy-release rates associated with the evolution of the surfaces in contact and the mass fluxes due to wear. They are used as characteristic quantities in the formulation of the wear criterion and wear velocities. Given that the physics of the interface modify the global contact conditions, micromechanical considerations are developed and result in an interface law, modeling its evolution with an internal parameter: the volume fraction of wear debris. The relation between this parameter and wear velocities is obtained with the mass conservation equation, which completes the model and allows to apply it in a numerical simulation. As an example, a problem of a rigid punch sliding on an elastic worn-out half-plane is treated by means of integral equations, accounting on the presence of an interface according to the previous modeling. Stresses and strains are obtained analytically, as asymptotic expansion fields.