In this master’s thesis we consider the p-spin spin glass model, in both its spherical and Ising versions, as a schematic model for amorphous solids. In the first part of the thesis, we briefly review the main properties of the spherical p-spin model, focusing in particular on the free energy landscape and the metastable/glassy states. We then introduce a model for studying the deformation of these glassy states, consisting in the addition of an s-spin term to the original p-spin Hamiltonian. This p + εs deformation is then studied by considering the Franz-Parisi potential, which allows us to follow the glassy states and study their stability under the external perturbation.Considering first the spherical p-spin, a rich phase diagram is found by varying the degree of annealing (Tg) and the value of s.