Magnetic shape memory alloys have been the subject of much research in recent years as potential high actuation energy multifunctional materials. They can be considered as continua that deform under mechanical and magnetic forces. The constitutive magnetization response of such materials is highly non-linear with magnetic field. A boundary value problem where Maxwells equations of the magnetostatic problem are coupled with the non-linear constitutive behavior is solved using finite element analysis. The numerical simulation reveals localization zones of the field variables, which appear due to loss of ellipticity of the magnetostatic problem. Stability analysis is performed by considering the characteristics of the magnetostatic field equations.