Shape memory effect associated with martensitic transformations is of the rapidly developing field in nanotechnologies, where industrial use of systems established on that effect provide greater flexibility on the nano-devices fabrication of various kind. And therefore it addresses questions to the phase transition phenomena at low-scale and 1 arXiv:2002.07132v1 [cond-mat.mtrl-sci] 4 Feb 2020 its limitations and control. In this report, we studied the crystal structure of tapered plates of Ti 2 NiCu alloy and the temperature T c at which the martensitic transition occurs. We demonstrated that T c has a strongly descending character as a function of the plate thickness h. The critical thickness value at which the transition completely suppressed is 20 nm. Moreover, the obtained results for T c (h) curves indicate the hysteretic nature of the transition. These findings open the pathway for size limits indication and regimes modulation where the alloy-based nano-mechanical devices can be tuned to operate more efficiently.