A continuum mechanical model is used to simulate cubic-to-tetragonal stress-induced phase transformations and variant reorientations in NiMnGa shape memory alloy single crystals. The model is based on a detailed description of the stored energy. Furthermore the energy dissipation due to phase transformations is taken into account via the maximum-dissipation principle. The results from the 3D numerical simulations are compared with laboratory experiments on a NiMnGa [001]-oriented single crystal cuboid shaped specimen.