High-load actuators based on shape memory alloys (SMAs) hold significant potential for industrial applications. When controlled precisely, such actuators are suitable for machine tool applications, including automated fine alignment of guiding rails or fine positioning of large workpieces. Unlike conventional SMA wire actuators, these devices have large cross-sections, operate under compressive loads, and generate high actuation forces. However, their accuracy is limited by the nonlinear material behaviour during the martensite-to-austenite phase transformation. Additionally, the large SMA cross-section results in considerable thermal inertia, leading to notable temperature gradients and spatial variations in phase fractions. To support the development of advanced control concepts, a comprehensive model of these actuators has been derived. The model introduces martensite fraction as a state variable to describe hysteresis in the phase transformation, utilising a Preisach model to capture the behaviour of the Ni₄₅Ti₅₀Cu₅ alloy. Thermomechanical properties such as heat capacity, thermal conductivity, thermal expansion, and temperature-dependent stress–strain behaviour were identified experimentally. A thermal lumped-parameter network model, coupled with a mechanical model, is developed to account for thermal gradients and axial stress distribution, providing accurate predictions validated by thermographic measurements. The material and hysteresis models can be applied to various high-load actuator configurations with similar alloy compositions.