This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elastoplasticity. A Unite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen, Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element.. Numerical examples of Unite-strain problems are. presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (C) 2014 Elsevier B.V. All rights reserved