In this paper, we present a novel hybrid dynamical model for hysteretic actuators consisting of spring-loaded Shape Memory Alloy (SMA) wires. The hybrid description is obtained by reformulating a set of physics-based ODEs resulting from the Müller-Achenbach-Seelecke (MAS) model of SMA material. Although the MAS model provides an accurate and consistent description of the system hysteresis, its use for simulation and control is limited due to the highly nonlinear and stiff nature of the resulting ODEs. By means of the hybrid reformulation, the numerical stiffness can be effectively eliminated while keeping all the benefits of the physics-based description. The different operating modes and transitions are first described from a physical point of view and then used to develop the flow and jump dynamics of the resulting hybrid model. Numerical simulations show that both hybrid and physics-based models provide nearly identical results. In addition, it is observed that the former requires simulation times that are up to two orders of magnitude smaller than the latter.