The pseudoelastic and pseudoplastic properties of NiTi alloys result from the closeness of the structures between the B2 cubic austenite and the B19' monoclinic martensite, and from the facility to transform one into each other. The paths followed by the atoms during the B2 → B19' transformation are usually imagined as combinations of simple shears and shuffles. Here, we propose a simplified hard-sphere atomistic model of phase transformation decomposed into three distinct types of rotational movements. The inputs are the Ti and Ni atomic diameters and the monoclinic angle β. The outputs are the lattice parameters and atomic positions of the B19' phase. The results are remarkably close to those reported in the literature. The model permits a better understanding of the B19' structure and the way it is inherited from its parent B2. The value of the monoclinic angle corresponds to the highest molar volume; which suggests that it could be a consequence of a maximization of the vibrational entropy. The hard-sphere model also successfully predicts the B19 structures reported in the binary alloys AuTi, PdTi, and AuCd. The agreement is less satisfying for the B19 structure observed in the ternary NiTiCu alloys. It is concluded that the B19' phase in NiTi alloys, and the B19 phase in AuTi, PdTi, and AuCd alloys can be considered as "simple" hard-sphere structures.