This paper presents some numerical simulations, aimed to the assessment of the structural performance of masonry walls, reinforced with FRP composite materials. The problem is modeled in two dimensions, and the effects of seismic loads and of foundation settlements are studied numerically. The tool we use to perform the numerical analysis, is a new minimization software developed by the authors to analyze masonry constructions, modeled as unilateral structures. The material model we adopt, no-tension with elastic–plastic (associated) behavior in compression, is path-dependent and rate-independent. The trajectory of the system, under a given loading history, is approximated as a sequence of minimizers of a path dependent form of energy, updated at each stage of the step-by-step, time-discretized procedure. The results we obtain confirm that the application of fiber reinforced composites must be done carefully, since the increase of strength in some structural elements, due to the retrofitting, may prevent the structure from developing its natural, stress relieving, kinematics.