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The magnetic shape memory effect, that is the rearrangement of martensitic microstructure induced by an external magnetic field, is of interest in many fields of application. The effect is based on a preceding martensitic transformation and provides a giant macroscopic strain. This change in length is induced by the complex interplay of magnetic and elastic energies. The effective free energy functional describing this effect is derived and employed in a phase-field model. The coupled equations of motion for the phase fields, the elastic displacement field and the spontaneous magnetization, follow on the energy minimizing principles. Numerical simulations with parameters reflecting the Ni₂MnGa material system show the general applicability of the aproach.