The mechanical behavior of shape memory alloys (SMAs) is closely related to the formation and evolution of its microstructures. Through theoretical analysis and experimental observations, it was found that the stress-induced martensitic transformation process of single crystal Cu-based SMA under uniaxial tension condition consisted of three periods: nucleation, mixed nucleation and growth, and merging due to growth. During the nucleation, the stress dropped rapidly and the number of interfaces increased very fast while the phase fraction increased slowly. In the second period, both the stress and the interface number changed slightly but the phase fraction increased dramatically. Finally, the stress and the phase fraction changed slowly while the number of interfaces decreased quickly. Moreover, it was found that the transformation could be of multi-stage: sharp stress drops at several strains and correspondingly, the nucleation and growth process occurred quasi-independently in several parts of the sample.