This paper presents a formulation of the transient response of elastomeric rods with embedded shape memory alloy actuators that incorporate the inherent coupling between the dynamics of deformation at the structural level, the thermal response and the constitutive law describing the shape memory alloy. Previous work by the authors has shown that the incorporation of shape memory alloy actuation in distributed parameter systems can induce a large class of nonlinearities including hysteresis effects in the SMA constitutive law, nonlinear kinematics of large deformation, and, in some cases, local plasticity effects. To derive a control methodology for the class of SMA embedded elastomeric rods considered in this paper, it is essential that the system characteristics of the nonlinear distributed parameter system be identified accurately. This paper presents an identification theory applicable to the coupled system of partial differential equations. The results are validated using both numerical simulation and experimental results.