Crack growth in a homogeneous elastic solid under impact shear loading conditions is analyzed numerically, with the crack constrained to grow along a weak plane directly ahead of the initial crack tip. The configuration analyzed is a plane-strain model of that used in the experiments of Rosakis et al. (1999). A cohesive surface constitutive relation is specified along the weak plane that relates the tractions and displacement jumps across it and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any additional failure criterion. The effect of cohesive strength and impact pulse time on the response is explored. In a certain parameter regime, the calculations reproduce, at least qualitatively, the type of crack speed histories seen in the experiments. For other parameter values, an abrupt transition from crack growth at the Rayleigh wave speed to a value above 2 times the shear wave speed is seen. This transition involves microcrack nucleation ahead of the main crack. At intersonic crack speeds, shock-like gradients in the near-tip stress field are found as seen in the experiments.