In the presented paper, a sample of polycrystalline shape-memory NiTi alloy is studied under compression up to 5% by the means of laser-excited and laser-detected ultrasound waves. The evolution of a propagation velocity of the surface acoustic wave is measured in situ during mechanical loading. An inverse method based on the Ritz-Rayleigh numerical approach is then used to obtain the development of elastic properties of the sample. This process enables an analysis of the evolution of stress-induced transformation from the austenitic to the martensitic phase with the possibility to describe several stages of such transformation, i.e., the transformation to full R-phase, its reorientation causing strong anisotropy of the polycrystalline sample, and consecutive gradual transition to martensite.