In this paper three models of the shape memory alloy behaviour have been presented and re-investigated. The models are attributed to Tanaka, Liang and Rogers, and Brinson, and have been used extensively in the literature for studying the static or dynamic performance of different composite material structures with embedded shape memory alloy components. The major differences and similarities between these models have been emphasised and examined in the paper. A simple experimental rig was designed and manufactured to gain additional insight into the main mechanics governing the shape memory alloy (SMA) mechanical properties. Data obtained from the experimental measurements on Ni–Ti wires have been used in the numerical simulation for validation purposes. It has been found that the three models all agree well in their predictions of the superelastic behaviour at higher temperatures, above the austenite finish temperature when shape memory alloys stay in the fully austenitic phase. However, at low temperatures, when the alloys stay in the fully martensitic phase, some difficulties may be encountered. The model developed by Brinson introduces two new state variables and therefore two different mechanisms for the instigation of stress-induced and temperature-induced martensite. This enables more accurate predictions of the superelastic behaviour. In general, it can be recommended that for investigations of the shape memory and superelastic behaviour of shape memory alloy components the Brinson model, or refinements based on the Brinson model, should be applied.