The non-linear dynamic thermomechanical behaviour of superelastic shape memory alloys is investigated. To this end, the Zaki–Moumni model, initially developed for quasi-static loading cases, is extended to simulate the uniaxial forced oscillations of a shape memory alloy device. First, the influence of loading rate is accounted for by considering the thermomechanical coupling in the behaviour of NiTi shape memory alloy. Comparisons between simulations and experimental results show good agreement. Then, the forced response of a shape memory alloy device is investigated at resonance. Both isothermal and non-isothermal conditions are studied, as well as non-symmetric tensile-compressive restoring force. In the case of large values of forcing amplitudes, simulation results show that the dynamic response is prone to jumps, bifurcations and chaotic solutions.