The temperature dependence of ordinary magnetostriction of the axially compressed Ni–Mn–Ga alloy with the low values of shear elastic modulus C'(T) ~ 1 – 10 GPa has been evaluated theoretically in the framework of Landau theory. The computations showed that the compression with 50 MPa stress reduces the ordinary magnetostriction by factor 3 at room temperature. Nevertheless, the magnetostriction of compressed alloy exceeds the value of 10–4 in the whole temperature range of martensitic phase stability, strongly depends on the temperature in the vicinity of martensitic transformation (MT), and is practically constant well below MT temperature. Therefore, the purposeful search for the alloy with the low value of shear elastic modulus and high MT temperature (well above 300 K) may result in the discovery of good magnetostrictive material. This material will posses the temperature-independent magnetostriction value about of 10–4 –10–3 and rather low electric conductivity enabling the technical applications of this material in dynamic regimes.