A magnetoelectric memory element includes a magnetic element having an easy magnetization axis aligned along a first axis, means for applying to the magnetic element a magnetic polarization field aligned along a second axis not parallel to the first axis, a piezoelectric or electrostrictive substrate mechanically coupled with the magnetic element, and first and second electrodes arranged to apply an electrical field to the substrate so that the substrate exerts, on said magnetic element, a non-isotropic mechanical stress of a main direction generally oriented along a distinct third axis coplanar with the first and second axes. The magnetic element exhibits, by a combined effect of the magnetic polarization field and the easy magnetization axis, two distinct states of stable equilibrium of magnetization, corresponding to two not mutually opposed magnetization directions. The non-isotropic mechanical stress is sufficiently intense to induce a switchover between the two distinct states.