The study of the thermal stability of Ni3Al nanoneedles in the dependence on the sharpness and crystallography orientation of the needle axis was held using molecular dynamics method. It is shown that the most stability nanoneedles in the conditions of thermal influence are the ones with the axis along [111] direction. Violation of the nanoneedles stability associated with their blunting, which is caused by surface diffusion. Stable radius of curvature of the needles at low temperatures, depending on the angle of the tip and orientation of the needle axis, is 0.6-1 nm.