Shape memory materials represent a promising class of dual-shape materials that can move from one shape to another in response to a stimulus such as light, heat, electricity or magnetism. In this regard, the biomedical field is showing large interest in this class of materials, especially in shape memory polymers (SMPs), whose mechanical properties make them extremely attractive for many biomedical applications. However, diverse characteristics including also the mechanical behaviour are still part of research. In this contribution the shape memory properties of polymers will be quantified by cyclic thermomechanical investigations. One cycle includes the "programming" of the sample and the recovery of its permanent shape. To describe this phenomenon, a three-dimensional thermomechanical coupled model is proposed. This macromechanical constitutive model is based on the physical understanding of the material behaviour and a mechanical interpretation of the stress-strain-temperature changes observed during thermomechanical loading. The main focus of this work is the influence of both, the material constants and heat transfer boundary conditions on the response of shape memory polymers. Therefore we illustrate different general simulations as well as examples of application.