Standard approaches to magnetomechanical interactions in thermal magnetic crystalline solids involve Landau functionals in which the lattice anisotropy and the resulting magnetization easy axes are taken explicitly into account. In glassy systems one needs to develop a theory in which the amorphous structure precludes the existence of an easy axis, and in which the constituent particles are free to respond to their local amorphous surroundings and the resulting forces. We present a theory of all the mixed responses of an amorphous solid to mechanical strains and magnetic fields. Atomistic models are proposed in which we test the predictions of magnetostriction for both bulk and nanofilm amorphous samples in the paramagnetic phase. The application to nanofilms with emergent self-affine free interfaces requires a careful definition of the film “width” and its change due to the magnetostriction effect.