A method is presented for the analysis of the transmitted and reflected transient elastodynamic wavefield at a fracture that may be modeled as a linear slip interface. This interface model implies that the traction is continuous at the fracture, while the displacement may show a jump discontinuity that is proportional to this local traction. To start with, for both the SH and the P/SV wave systems, transform domain expressions are determined for the transmitted and reflected wavefields at the interface. Subsequently, an almost completely analytical transformation back to the space-time domain is carried out. The method provides the exact time domain transmitted and reflected waves (including the body wave, interface wave, and head wave contributions) that are caused by a spatially curved, incident wavefield due to a point source. Various numerical results are given. For the SH case, the directionally dependent filter behavior of the fracture is shown. For the P/SV case, first the reflection, transmission, and conversion of body waves is presented. The next set of results involves the interface wave contribution and includes pictures of the particle movement on both sides of the fracture. Finally, the presence of headwaves in case of SV->P and SV->SV reflection is shown.