The shape of memory phase transformation in Ni-Ti was studied using tubes and wires of near equiatomic composition. The emphasis was on the effect of stress as produced by an applied uniaxial tensile stress and as a result of prior transformation fatigue cycling, TFC (cycling through the transformation under combined variations in temperature and stress). Measurements were made of strain and resistivity versus temperature and of tensile properties. The transformation volume change was also investigated at zero applied stress by hydrostatic weighing and strain gage measurement;The primary observation, made for both Ni-Ti tubes and wires, was that the axial transformation strain increases with increasing applied tensile stress. This increase is interpreted in terms of the effect of the applied stress to establish preferred directions of transformation shear during transformation to the low temperature phase. Upon the reverse transformation on heating, the strains are reversed. Other effects of the applied tensile stress are to increase the martensite start (M(,S)) and austenite start (A(,S)) temperatures and to increase the resistivity of the low temperature phase;The relative transformation volume change on cooling was measured by hydrostatic weighing to be 0.19 percent and was deduced by the strain gage measurements to be about 0.22 percent. By contrast, earlier lattice parameter measurements of the high temperature B2 phase and low temperature distorted B19 phase indicate about -0.5 percent, thus a volume decrease upon transformation. Several possible explanations for the discrepancy are discussed;Prior high-level TFC into the millions of cycles causes a decrease in the applied stress dependence of the total transformation strain, of M(,S) and A(,S), and of the low temperature phase resistivity. Earlier work has shown that transformation cycling introduces dislocations, and these are believed to mask the effects of the applied stress;Tensile tests were conducted on uncycled and TFC'd wires, mostly in the high temperature phase. The prior TFC was found to cause an increase in yield stress and a decrease in future strain. In this respect, the effect of prior TFC is considered to be similar to that of prior cold working;Annealing at 400(DEGREES)C following the high-level TFC produces a partial restoration of the transformation and tensile properties characteristic of uncycled wires. Annealing at 600(DEGREES)C produces full restoration.