This paper aims to adapt the well established Brinson model for the thermoelastic behaviour of the Shape Memory Effect (SME) so as to compare it to a custom shape memory material modelled using an finite element modelling software. In this work, the Brinson model is further adapted so as to obtain an analytical model of a bias-spring shape memory alloy (SMA) actuator which consists of a SMA attached in series to a spring. This type of SMA actuator allows for the SMA to be cyclically actuated by heating and cooling. The dimensioning of bias-spring that is attached to the SMA is crucial for the actuating of the system. The adapted model presented in this work allowed for the analysis of the various design parameters when creating such an actuator while also allowing for an optimal dimensioning of the spring system so as to maximise the stroke of the actuator when activated.