The effect of a magnetic field on martensitic transformations in Fe–Ni–Co–Ti and Fe₃Pt shape memory alloys has been examined in order to know a magnetic field-induced martensitic transformation and a control of crystallographic domain (variant) by magnetic field. Following results were obtained: (i) Magnetoelastic martensitic transformation (martensites are induced only while a magnetic field is applied and are transformed back to the parent phase when the magnetic field is removed.) appears in an ausaged Fe–Ni–Ti–Co shape memory alloy. The critical magnetic field for inducing a magnetoelastic martensitic transformation increases with increasing temperature. Volume fraction of martensite induced depends on the strength of the magnetic field. (ii) Magnetic field controls perfectly the crystallographic domain (variant) in a martensite state of an ordered Fe₃Pt, which exhibits a martensitic transformation from a cubic parent phase to a tetragonal martensite phase. In addition, a giant magnetostriction of about 5×10⁻³ was realized under a magnetic field of up to 3.2 MA/m, which is nearly three times as large as that of Terfenol-D (Fe₂Dy_xTb_1−x).