Magnetic shape memory (MSM) alloys, which transform martensitically below the Curie temperature in the ferromagnetic (FM) state, represent a new class of actuators. In Ni2MnGa, unusually large magnetic field-induced strains of about 10% have been observed. This effect is related to a high mobility of martensitic twin boundaries in connection with a large magneto-crystalline anisotropy. MSM materials exist in a variety of different martensitic structures depending on temperature and compositions. We investigate the energetics of L10 phase twin boundary motion quasi-statically with ab initio methods and relate the results to calculations of the magneto-crystalline anisotropy energy. Our results indicate that for the L10 structure the energy needed for a coherent shift of a twin boundary may be too large to be overcome solely by magnetic field-induced strains.