We have made an energy evaluation for the rearrangement of martensite variants (RMV) under a magnetic field using four types of ferromagnetic shape memory alloys: an Fe-31.2at. %Pd with so-called fct martensite, a Ni
_2
MnGa with the 10 M martensite, a Ni
_{2.02}
Mn
_{1.09}
Ga
_{0.89}
with the 14 M one and a Ni
_{2.14}
Mn
_{0.92}
Ga
_{0.94}
with the 2 M one. The RMV by a magnetic field occurs at any temperature for the Fe-31.2Pd and the 10 M martensite. However, it occurs in a limited temperature range for the 14 M martensite and does not occur at any temperature for the 2 M martensite. The reason of such different behavior is quantitatively explained by evaluating two shear stresses: the magnetic shear stress acting across a twinning plane τ
_{mag}
, and the stress required for the twinning plane movement τ
_{req}
. That is, by comparing the value of τ
_{mag}
and τ
_{ req}
thus evaluated, we have confirmed that the following condition is universal regardless of temperature, field direction and structure of the martensite phase: the value of τ
_{mag}
is larger thanτ
_{req}
when the RMV occurs by magnetic field and vice versa.
