A coupled kinetic Monte Carlo – Finite Element Analysis (kMC–FEA) method is developed with a numerical implementation in the Scalable Implementation of Finite Elements at NASA (ScIFEN). This method is presented as a mesoscale model for Shape Memory Alloy (SMA) material systems. The model is based on Transition State Theory and predicts the nonlinear mechanical behavior of the 1st order solid–solid phase transformation between Austenite and Martensite in SMAs. The kMC–FEA modeling method presented in this work builds upon the work of Chen and Schuh [1, 2]. It represents a “bottom-up” approach to materials modeling and could serve as a bridge for future studies that attempt to link ab initio methods with phenomenological findings in SMA systems. This thesis presents the derivation of the kMC–FEA model, which is then used to probe the various responses expected in SMAs and verify the influence of model parameters on simulation behavior. In a departure from the work of Chen and Schuh, the thermodynamic derivation includes an elastic transformation energy term, which is found to be a significant fraction of the total transformation energy and play an important role in the evolution of a simulation. Theoretical predictions of the model behavior can be made from this derivation, including expected transformation stresses and temperatures. A convergence study is presented as verification that the new elastic energy term proposed in this model is a reasonable approximation. A parameter sensitivity study is also presented, showing good agreement between theoretical predictions and the results of a full-factorial numerical exploration of model outputs. Model simulation demonstrates the emergence of the shape memory effect, an important SMA behavior not shown by Chen and Schuh, along with the expected superelastic effect and thermal hysteresis. Further exploration of simulated model outputs presented in this work involves comparison with experimental data and predicted output values obtained from a separate phenomenological constitutive model. This comparison shows that the kMC–FEA method is capable of reproducing qualitative, but not yet quantitative, responses of real SMA material systems. Discussion of each model parameter and its effects on the behavior of the model are presented as guidelines for future studies of SMA materials. A complete implementation of the method is contained in a new finite element software package (ScIFEN) that is available for future