Owing to their high energy densities, smart materials like shape memory alloys (SMAs), Macro-Fiber Composites (MFCs) and, electroactive polymers (EAPs) have massive potential as actuators in wing morphing applications. In this article, a detailed numerical model is developed for the shape prediction of an elastic base that is actuated by a combination of a shape memory alloy (SMA) wire and a Macro-Fiber Composite (MFC) bimorph. It has been demonstrated using the model that it is possible to achieve large deflections at low frequencies by virtue of the phase transformations in the SMA wire and rapid actuation with small deflections due to the MFC bimorph. In the developed scheme, the elastic base is modeled using non-linear Euler-Bernoulli beam theory. The influence of the non-linear hysteresis in the SMA wire and the linear actuation characteristics of the MFC is studied by incorporating thermo-mechanical and electro-mechanical constitutive behavior into the non-linear beam theory. The system of coupled equations hence obtained, is solved iteratively to obtain the deflected shape of the elastic base. The results from the developed numerical scheme are validated against the previously available studies in the literature and experiments. Additionally, the synergistic advantage of using the two actuators together has been shown through experiments. As an illustration, a smart trailing edge camber morphing concept is developed by integrating the flexible elastic structure along with the two smart actuators to a NACA 0012 airfoil as the trailing edge. © 2020 IOP Publishing Ltd.