Shape memory alloys have been used almost exclusively in components subjected to simple loadings such as uniaxial tension, pure bending or torsion. As part of the development of smart structures and adaptive components, shape memory alloys must be designed to function in complex, multi-dimensional stress states. In order for these materials to participate as active elements in smart structural designs, the alloys must undergo a phase transformation, during which their properties change. For 1D stress states, data generated in simple stress-strain- temperature tests is sufficient to define the onset and completion of a phase transformation. When multi-dimensional stress states are encountered, data from more complicated tests will be needed to define the transformation. In this paper, a model for multi-dimensional phase transformation criteria is introduced and discussed, and tests for defining the boundaries of the initiation and completion of phase transformation surfaces are proposed.