Magnetic shape memory alloys (MSMAs) are relatively new materials that exhibit a magnetic shape memory effect as a result of the rearrangement of martensitic variants under the influence of magnetic fields. Due to the MSMAs newness there is limited understanding of their magneto-mechanical behavior. This work presents experimental and modeling results of MSMAs for cases in which the material is loaded and unloaded in uniaxial compression in the presence of a constant magnetic field. The experiments are performed with the magnetic field applied perpendicular and at an angle to the mechanical loading axis. During the loading and unloading process, the evolution of the magnetic flux density is monitored to assess the potential of these materials for power harvesting applications. The modeling is based on the thermodynamic approach proposed by Kiefer and Lagoudas . This model was modified and calibrated to reproduce material response under biaxial constant magnetic field and variable uniaxial compressive stress. Comparing the experimental and simulated results, one can recognize that further work is needed to improve the model.