A method is presented for the analysis of the transmitted and reflected transient elastodynamic wave field at a fracture that may be modeled as a linear slip interface. With this method, the space-time domain problem is first carried over to the transform domain by means of a temporal Laplace transformation and a two-dimensional, horizontal spatial Fourier transformation. Subsequently, for both theSHand theP/SVwave systems, expressions are determined for the transmitted and reflected wave fields at the interface. Afterward, a transformation back to the space-time domain is carried out. The method is capable of providing the exact transmitted and reflected waves (including the body wave, interface wave, and head wave contributions) that are caused by a spatially curved, incident wave field due to a point source. Moreover, it is especially designed to yield the time domain waveforms. Various exact numerical results are given. For theSHcase, the directionally dependent filter behavior of the fracture is shown. For theP/SVcase, first the reflection, transmission, and conversion of body waves is presented. The next set of results concerns the interface wave contribution and includes pictures of the particle movement on both sides of the fracture when either the transversal or the normal specific compliance of the fracture is equal to zero. Finally, the presence of head waves in case ofSV→PandSV→SVreflection is shown.