In this study, the simulation of the motion of an interface during the stress-induced martensitic transformation of a shape memory alloy is performed using the level-set method. The kinetics of the phase transformation is defined as an anisotropic kinetic relation between the rate at which the weak discontinuity moves, given by its normal velocity, and the thermodynamics driving force. The latter is derived from a dissipation function, which obeys the 1st and 2nd law of thermodynamics and accounts for large strains. Furthermore, a hyperelastic constitutive framework is used to describe the constitutive behavior of the material. The model is implemented into the finite element method and is then used to solve a 2D phase transformation problem in a shape memory alloy.