A ray method is presented to analyze elastodynamic radiation generated by slip over a fault plane. With this mehtod, either the discontinuities at the wave fronts or, equivalently, the high-frequency components of the fields can be calculated. The method is applied to the computation of ground motions generated by crack propagation models for earthquake faulting. It is very suitable for computing strong motions produced by abrupt changes of speed of the rupture front. Basic to the method are two canonical solutions for elastodynamic radiation which correspond to sudden changes of the rupture speeds of semi-infinite cracks propagating in the mode 2 and mode 3 fracture modes, respectively. When the rupture front of a slip zone suddenly changes speed, each point on the rupture front produces fans of rays of longitudinal and transverse motion, respectively. The method appropriately combines the mode 2 and mode 3 canonical solutions on the diffracted rays, and it provides corrections for curvature of the rupture front. Particular attention is devoted to the focusing of motion due to curvature of the rupture front. The results relate the intensity of the radiated fields to the nature of the slip just behind the rupture front.