The diffraction of a cylindrical longitudinal pulse by a semi-infinite crack is studied analytically using integral transform techniques and the Wiener-Hopf method. The inverse transformations are performed by an extension of the Cagniard-de Hoop technique that enables three successive inversions to be performed in one step rather than the usual two successive inversions. Examination of both the reflected and diffracted displacements near the transverse-wave reflection boundary indicates the presence of a transition disturbance. Such a disturbance is not found if the incident pulse is plane or if the elastic solid is replaced by a medium supporting only one wave type such as an inviscid fluid. Asymptotic approximations to the most important diffracted pulses, that are valid near their wave fronts, are given and are compared with those predicted by the geometrical theory of diffraction.