The objective of this article is the modelling and the numerical simulation of the response of elastoplastic structures to impacts. To this end, a numerical method is proposed that takes into account one-sided contact (Signorini condition) and impact phenomena together with plasticity in a monolithic solver, while accounting for the non-smooth character of the dynamics. The formulation of the plasticity and the contact laws are based on inclusions into normal cone of convex sets, or equivalently, variational inequalities following the pioneering work of Jean Jacques Moreau (1974) and Halphen and Son Nguyen (1975), who introduced the assumptions of normal dissipation and of generalised standard materials (GSM) in the framework of associated plasticity with strain hardening. The proposed time-stepping method is an extension of the Jean and J. J. Moreau (1987) scheme for nonsmooth dynamics. The discrete energy balance shows that spurious numerical damping can be removed and the scheme is practically unconditionally stable. Furthermore, the finite-dimensional variational inequality at each time-step is well-posed, can be solved by optimisation methods for convex quadratic programs, providing an interesting alternative to the return mapping algorithm. The paper is completed by numerical illustrative examples of impacts on metallic structures made of beams.