Shape memory alloys (SMAs) have interesting properties for application in adaptive structures, and many researchers have already explored their possibilities. However, the complex behavior of the material makes the development of SMA adaptive structures a challenging task. It is generally accepted that systematic, model-based design approaches and design optimization techniques can be of great assistance in this case. Although some studies on design optimization of relatively simple SMA structures have been published, formal design optimization of more complex SMA devices still requires further exploration. By considering a typical example, i.e. an active catheter, the present paper aims to provide new insights into and solutions for the problems encountered in the practical application of model-based design approaches to SMA adaptive structures. Active catheters are equipped with integrated micro-actuators that enable controlled bending, which yields enhanced maneuverability compared to conventional catheters. Next to a detailed discussion of an SMA active catheter finite element model, a novel SMA constitutive model is introduced. This model combines an adequate representation of the experimentally observed behavior with computational efficiency. Moreover, its history-independent nature significantly simplifies sensitivity analysis. Due to these features, application of optimization techniques to shape memory alloy adaptive structures becomes a realistic possibility.