Abstract <p>Some mechanical properties of magnetostrictive material galfenol (Fe–Ga alloy) are described. This alloy is machinable, ductile and resistant with respect to corrosion and exhibits improved mechanical properties. Experimental results for measuring Young’s modulus and Poisson’s ratios along different crystallographic directions under mechanical tension affecting a galfenol single crystal are presented. The anisotropy of the elastic properties inherent in a BCC galfenol crystal is described. It is shown that along some directions, galfenol has a negative Poisson’s ratio, i.e., it behaves like an auxetic. Theoretical conditions for obtaining negative Poisson ratios in BCC metals and the calculated values of the Poisson ratios and Young’s modulus for galfenol are given. “Planar” auxetic galfenol characteristics are considered, some examples of galfenol application as a base of fastening units are presented.</p>