To study martensitic phase transformation we use a micromechanical model based on statistical mechanics. Employing lattice Monte-Carlo simulations and realistic material properties for shape-memory alloys (SMA), we investigate the combined influence of the external stress, temperature, and interface energy between the austenitic and martensitic phase on the transformation kinetics and the effective material compliance. The one-dimensional model predicts well many features of the martensitic transformation that are observed experimentally. Particularly, we study the influence of the interface energy on the transformation width and the effective compliance. In perspective, the obtained results might be helpful for the design of new SMAs for more sensitive smart structures and more efficient damping systems.