This program generates sets of ray-theoretical seismograms for an incident plane wave (teleseismic approximation) for models consisting of a stack of layers with planar but nonparallel (dipping) interfaces, allowing the possibility of anisotropy in the layers. Incident P and S waves are supported. PyRaysum is a Python wrapper around the Fortran software Raysum, originally developed by Andrew Frederiksen. Although a trimmed down version of the Fortran code is supplied with PyRaysum, you can find the original version here.