Abstract We discuss, within a framework in which the structural degrees of freedom (assumed essentially three-dimensional) are adiabatically treated and the magnetic degrees of freedom are exactly treated (as far as the disordered-phase results and the second order critical frontiers are concerned), the stress-(magnetic) field-temperature phase diagram associated with the one-dimensional first-neighbour spin- 1 2 magneto strictive XY model. The important influence of the curvature of the coupling constant as a function of distance is exhibited and satisfactorily compared to experimental data.