This paper presents a prestressed sliding wedge damper as an effective alternative for the reduction of vibration amplitudes. Due to the system's non-smooth and non-linear characteristics, it offers advantages over conventional linear dampers, e.g an amplitude adaptive behavior. First, the equations of motion which describe the system's characteristics are derived. Second, an analytical model based on a modal coordinate transformation and averaging methods is proposed. A numerical model, which uses an elasto-plastic contact model is set up, in order to fully model the systems behavior. An analysis of the dampers characteristics shows that it is a pseudo-viscous damper realized via dry friction. The analytical and numerical results are compared and show a reasonable agreement, as within asymptotic methods. This work presents the first investigations into prestress influence on such a damper and offers insight into future theoretical, numerical, and experimental analysis.