Revisited Simo algorithm for the plane stress state.

•The differential type elasto-plastic model with mixed hardening describing the in-plane stress state.•The update algorithm to solve the model, based on the radial return algorithm adapted to the in-plane stress.•The discretized weak formulation of the non-linear elastic-type problem; finite element implementation.•The algorithmic elasto-plastic tangent moduli rebuilt to solve the non-linear system for displacements.•Comparison of the Simo solution and the in-plane stress solution applied to a trapezoidal plate.