An analytical solution is presented for the atomic displacements in the steady motion of a dislocation in a modified Frenkel‐Kontorova model of the form treated previously by Atkinson and Cabrera. It is found that at a critical dislocation velocity, here termed the breakdown velocity, &ngr;B, the regular dislocation motion postulateda prioribreaks down, so that the analytical solution is not valid for dislocation velocities &ngr; ≥ &ngr;B. Furthermore, &ngr;Bis less than the corresponding macroscopic sound velocity for this model. The results of computer‐simulation studies of the behavior of the model at stress levels greater than those which cause dislocation breakdown are also presented.