Recently, Ti-Ni based intermetallic alloys with shape memory effect (SME) have attracted much attention as promising functional materials for the development of record small nanomechanical tools, such as nanotweezers, for 3D manipulation of the real nano-objects. The problem of the fundamental restrictions on the minimal size of the nanomechanical device with SME for manipulation is connected with size effects which are observed in small samples of Ti-Ni based intermetallic alloys with thermoplastic structural phase transition from austenitic high symmetrical phase to low symmetrical martensitic phase. In the present work, by combining density functional theory and molecular dynamics modelling, austenite has been shown to be more stable than martensite in nanometer-sized TiNi wafers. In this case, the temperature of the martensitic transition asymptotically decreases with a decrease in the plate thickness h, and the complete suppression of the phase transition occurs for a plate with a thickness of 2 nm, which is in qualitative agreement with the experimental data. Moreover, the theoretical values obtained indicate the potential for even greater minimization of nanomechanical devices based on SME in TiNi.