- The magnetically induced martensitic variant reorientation process under applied mechanical load in magnetic shape memory alloys (MSMAs) is considered. Of particular interest is the associated nonlinear and hysteretic macroscopic strain response under variable applied magnetic field in the presence of stress, also known as the magnetic shape memory effect (MSME). A thermodynamically consistent phenomenological constitutive model is derived which captures the magnetic shape memory effect caused by the martensitic variant reorientation process, using internal state variables, which are chosen in consideration of the crystallographic and magnetic microstructure. The magnetic contributions to the free energy function considered in this work are the Zeeman energy and the magnetocrystalline anisotropy energy. Activation functions for the onset and termination of the reorientation process are formulated and evolution equations for the internal state variables are derived. The model is applied to a two-dimensional special case in which the application of a transverse magnetic field produces axial reorientation strain in a NiMnGa single-crystal specimen under a constant compressive axial stress. It is explicitly shown how the model parameters are obtained from experimental data. Model predictions of magnetic field-reorientation strain hysteresis loops under different applied stresses are discussed.