The ferromagnetic shape memory alloys (SMAs) attract considerable attention of researchers mainly because they proved to be easy deformable by a moderate magnetic field. The record-breaking magnetic field-induced strain (MFIS), ε % 12 %, was induced recently in the ferromagnetic Heusler-type Ni-Mn-Ga alloy by the external magnetic field H % 10 kOe [1].Historically, as early as in 1996, the nearly 0.2 % strain was induced by the magnetic field application to the Ni-Mn-Ga single crystal [2]. As it was noticed by the authors of the pioneer work [2], the observed value of MFIS was too large, to be attributed to the magnetostriction which is inherent to all magnetically ordered solids. In this connection, the idea about the strong influence of the moderate magnetic field on the microstructure of internally twinned alloy via the magnetically induced mechanical stress (magnetostress) was put forward [2][3][4]. Furthermore, it was shown that the magnetostress is caused by the magnetoelastic interaction [5,6].The most studied ferromagnetic SMAs belong to the Heusler Ni 2 MnGa compound and its off-stoichiometric analogues. Basically, these alloys exhibit the