We propose a phenomenological model for the evolutionary behaviour of shape memory alloys, where the possibility of plastic deformation is taken in to account. Two dissipative mechanisms are considered, namely the dissipation associated with solid-solid (martensitic) phase transformations and plastic dissipation. The plastic contribution may lead to an irreversibility of the evolution. The existence of a so-called energetic solution is established for a suitable relaxation of the problem in the spaceof Young measures. 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.