A Ni-Mn-Ga ferromagnetic shape memory alloy was tested for strain versus applied field and strain versus stress. Field- induced strains up to 6 percent were measured with a hysteresis of about 160 kA/m. The results are compared with the predictions of modeling with a focus on hysteresis. The model is applied to the case in which the magnetic external field and external load are orthogonal to each other. It predicts the magneto-mechanical hysteresis as a function of the yield stress in a twinned martensite. Magnetization versus applied field was measured on a sample that was mechanically constrained in order to understand the magnetization behavior of the sample in the absence of twin motion. These measurements give the magnetic anisotropy and are used to estimate the demagnetization fields. The measured behavior of strain with stress at constant field is approximated by the model.