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.