Shape Memory Alloy (SMA) is a distinctive type of smart material that exhibits substantial strain recovery on account of martensitic transformation induced by stress and temperature. To accurately model SMA-based structures, two critical factors must be addressed: the effect of finite deformation and the consequential material-level coupling induced by transformation. This study incorporates these factors by considering the thermodynamical material model of Lagoudas [1]. It incorporates the Jaumann stress rate for large deformation and considers thermoelastic and latent heat effects in the heat equilibrium equation. An incremental-iterative finite element framework is utilized to solve the equilibrium equations in the Updated Lagrangian framework. Finally, the response of an SMA-based stent unit cell and spring coil is simulated following the developed finite element (FE) formulation, demonstrating its efficacy.