The goal of this project is to reveal the potential of mixed finite element approaches based on first-order system least squares formulations for finite elasto-plastic deformations in nonlinear solid mechanics. This rests upon recent and ongoing work of the participating investigators studying stress-displacement first-order system approaches for small-strain elasto-plasticity and finite (hyper-)elasticity. The interest in this class of methods is driven by the need of accurate stress approximations with good momentum balance properties observed in various high-tech applications, as for instance from the automobile or aircraft industry (e.g. light-weight constructions) or from biomedical research (e.g. arterial wall/stent simulations). To the best knowledge of the authors there are no reliable and verified approaches for finite elasto-plasticity computations available at the moment and the main incentive of this project is to contribute in closing this gap.