It has been found in numerical simulation by Andrews <1976> that a growing mode II shear crack may at first rapidly accelerate toward the Rayleigh wave speed vR and then after a short period of readjustment start running at a speed slightly greater than (2)1/2vS, where vS is the shear wave speed. In order to throw some light on this phenomenon we study in detail the steady motion of a semi-infinite crack which is driven by a following point load which remains at constant distance d from the crack tip. A cohesive traction which is a function of relative displacement acts in the Dugdale type tip region which is small in comparison with d. We consider crack speeds vC in the range vCp, the p wave speed, and find that for vCR and for vSC< (2) 1/2vS the load is a decreasing function of vC, while for (2)1/2vS Cp the load increases with vC. The former situation is interpreted as instability, and the latter as stability. The range vRCS appears to be forbidden. This is in agreement with, and partially explains, Andrew's results. It also agrees with an earlier analytic solution obtained by Craggs <1960> for vCR. We find that for vCR the displacement in the tip region has a shape independent of vC but suffers a contraction analogous to a Lorentz contractionso that the length goes to zero as vC↑vR.