We present a seismological technique for determining the down-dip shape of seismogenic normal faults. Synthetic models of non-planar source geometries reveal the important signals in teleseismic P and SH waveforms that are diagnostic of down-dip curvature. In particular, along-strike SH waveforms are the most sensitive to variations in source geometry, and have significantly more complex and larger-amplitude waveforms for curved source geometries than planar ones. We present the results of our forward-modelling technique for 13 earthquakes. Most continental normal-faulting earthquakes that rupture through the full seismogenic layer are planar and have dips of 30°–60°. There is evidence for faults with a listric shape from some of the earthquakes occurring in two regions; Tibet and East Africa. These ruptures occurred on antithetic faults, or minor faults within the hanging walls of the rifts affected, which may suggest a reason for the down-dip curvature. For these earthquakes, the change in dip across the seismogenic part of the fault plane is ≤30°.