The potential use of Cu-based shape memory alloys (SMA) in retrofitting historical monuments is investigated in this paper. This study is part of the ongoing work conducted in Tunisia within the framework of the FP6 European Union project (WIND-CHIME) on the use of appropriate modern seismic protective systems in the conservation of Mediterranean historical buildings in earthquake-prone areas. The present investigation consists of a finite element simulation, as a preliminary to an experimental study where a cantilever masonry wall, representing a part of a historical monument, is subjected to monotonic and quasi-static cyclic loadings around a horizontal axis at the base level. The wall was retrofitted with an array of copper SMA wires with different cross-sectional areas. A new model is proposed for heat-treated copper SMAs and is validated based on published experimental results. A series of nonlinear finite element analyses are then performed on the wall for the purpose of assessing the SMA device retrofitting capabilities. Simulation results show an improvement of the wall response for the case of monotonic and quasi-static cyclic loadings.