The paper considers the issues of destruction of the working bodies of road-building equipment operated under conditions of abrasive wear with a fixed abrasive. Analytical studies of the influence of the tribological parameters of cutters on the intensity of their wear have been carried out. Based on the solution of the equations of the dynamics of the movement of the cutter in a viscoelastic medium, its geometric shape is optimized. The mathematical dependences of the influence of the geometric dimensions of the cutter on the pressure value and the intensity of tool wear are obtained.