Shape memory alloy (SMA) helical springs exhibit highly non-linear behaviour due to phase transformations unlike conventional elastic springs. They generally undergo large deflection with loading during which their mean coil diameter changes considerably, leading to geometrical non-linearity (GNL). Further, during loading and unloading, heating and cooling, change in phase of SMA spring causes change in material properties leading to material non-linearity (MNL). This material non-linearity includes variation in modulii and volume fraction depending on the phases and different zones within the phase. A new simple and generic formulation for instantaneous coil diameter is derived which require least number of input parameters and is independent of its phase. Accurate constitutive models are developed for predicting the mechanical response of SMA spring considering both GNL and MNL. Models are validated experimentally. Design and analysis of SMA springs carried out using the developed models. New SMA spring based actuator configuration is proposed.