Abstract: Scattering of a grazing longitudinal ultrasonic wave pulse by a traction-free ribbon-type crack in solid is analyzed theoretically in detail. An exact series solution of the scattered field is obtained by iteration. Each term of the series corresponds roughly to one of the rescattering processes by one of the crack tips. The first two terms, taken as the second order approximate solution, are discussed in detail. This approximate solution includes scattered cylindrical longitudinal waves, scattered cylindrical shear waves, head waves and surface waves on the crack surfaces, and gives good interpretation of the earlytime wave fields.