Shape memory alloys are used in many applications in engineering and medical fields. Their common practical implementations stem from their unique properties, which are the superelastic behavior and shape memory effect. While these characteristic effects are well understood from a physical standpoint, modeling of both effects in a thermomechanical fully coupled finite strain model is not straight forward. Our model [1,2] extends the model of Sedlak et al. [3] to the finite strain case, which allows to capture the shape memory effect as well as superelasticity. Further, we consider phase dependent thermal expansion as well as small volume changes due to the phase change, which occur in some high temperature shape memory alloys. One problem in modeling shape memory alloys is the constraint on the inelastic strains in the finite strain regime. Similar to plasticity, they should be volume preserving, which is motivated by the physics of the phase change. The presented model solves this using a projection ansatz presented in [4] for plasticity. Finally, we apply this model to a bistable shape memory alloy actuator.