In this article we study the existence theory to the Prandtl-Reuss dynamical model of elasto-perfect plasticity with non-homogeneous mixed boundary conditions. By using only the Yosida approximation of inelastic constitutive multifunction we are able to prove the existence of solutions without assuming any kind of safe-load conditions, which are quite common in the theory of elasto-perfect plasticity. (C) 2019 Elsevier Ltd. All rights reserved.