A method for structural dynamic contact problems with friction and wear is suggested. The method is obtained by including wear in the non-smooth contact dynamics method of Moreau. A comparison of the method to the discrete energy-momentum method of Simo and Tarnow is also outlined briefly. The fully discrete equations are treated using the augmented Lagrangian approach, where a non-smooth Newton method is used as the equation solver. Two two-dimensional examples are solved by the method. It is investigated how solutions of contact, friction and wear are influenced by inertia. It is shown that the quasi-static assumption might be questionable for solving contact problems with friction and wear. © 2003 John Wiley and Sons, Ltd.