The equation of motion and the stability conditions for cracks interacting with transversal waves and surface waves are given. Threshold conditions for crack propagation relate the crack to a critical duration of the pulse and a second condition gives a relation between initial pulse amplitude and crack length. For surface waves the influence of the length is overshadowed by the penetration depth of the wave. For longitudinal, as well as for transversal pulses, the pulse must have a least-action density in order to propagate a crack. This law loses its meaning for surface waves. Some applications of the derived results to fracture by earthquakes are indicated.