The problem of the uniform motion of a screw dislocation in a crystal is treated from the point of view of lattice dynamics. A simple model of cubic lattice with piecewise‐linear nearest‐neighbor interactions is considered in detail and the extension to more realistic interatomic forces is outlined. The external stress necessary to maintain the dislocation in uniform motion is computed as a function of dislocation velocity. This stress has a minimum at one‐half of the sound velocity and motion is quite possible at hypersonic velocities. The calculations are at zero temperature, hence the only dissipative mechanism present is the emission of phonons by the core of the moving dislocation. The theory is relevant to high‐velocity dislocation motion, which is not of the usual thermally activated type.