Shape memory alloys (SMA) can dissipate energy through hysteresis cycles without significant residual deformation. This paper describes the fabrication and testing of copper-based SMA hourglass-shaped plates for use in energy dissipation devices and the development of a numerical model to reproduce the experiments. The plates were tested under cyclic flexural deformations, showing stable hysteresis cycles without strength degradation. A detailed nonlinear numerical model was developed and validated with the experimental data, using as input the constitutive relationship for the material determined from cyclic tests of material coupons under tension loading. The model adequately reproduces the experimental results. The study is focused on the exploitation of SMA in the martensite phase.