The influence of the cooling/heating rate on the martensitic transformation temperatures and the strain variation in the quenched Ni-51 Ti-49 alloy was studied. It was found that a decrease in the cooling/heating rate increased the temperatures of the forward transformation. It was assumed that this was due to the fact that the Ni-51 Ti-49 alloy was able to undergo the forward transformation on cooling, as well as during isothermal holding, which increased the transformation temperatures on slow cooling. The influence of the cooling/heating rate on the transformation temperatures depended on whether the stress affected the cooling and heating or not. It was shown that if the forward transformation occurred under a constant stress, then the influence of the cooling/heating rate on its temperatures became weak. However, the temperatures of the reverse transformation under load depended on the cooling/heating rate and this dependence was more significant for the start temperature of the reverse transformation A(s) than for the finish temperature. It was found that the cooling/heating rate did not affect the shape memory effect, however, this influenced the irreversible strain depending on the stress acting on cooling and heating. It was assumed that this might be caused by different mechanisms of the oriented martensite appearance.