This article reports on two models for the shape memory effect and explains, how they are implemented in a finite element method program. The first model uses a phenomenological approach. For the example of a microgripper, the performance prediction of real actuators made of polycrystalline materials is demonstrated. In the second model, the martensite-austenite phase transition is treated as a thermodynamically activated process. Thermodynamic laws, like e.g. the minimization of the Gibbs free energy, are used for the formulation. To simplify the model, it is primarily intended to describe the behavior of single crystals. By comparing the simulated bending characteristic of a cantilever beam with experimental data, the applicability to polycrystalline material is tested. Due to the physics based formulation, this model gives more insight into the structural processes involved. This is very useful, e.g., for physical extensions needed for the simulation of the magnetic shape memory effect. It is shown, how the model can be extended to predict the behavior of actuators made of ferromagnetic Ni-Mn-Ga single crystals in a magnetic field.