Abstract An accurate, fast, and simple algorithm for 3D modelling of seismic edge diffractions is presented. It is based on a generalized Kirchhoff theory that applies also to inhomogeneous (non-uniform) media. Both the boundary values and the Green functions in the Kirchhoff diffraction integral are determined by dynamic ray tracing, and each ray event is treated separately to obtain a description with clear physical interpretation. For each event the resulting Kirchhoff diffraction integral is evaluated by means of a uniform asymptotic technique that remains valid for receiver points near shadow boundaries. Since all parameters needed in the computations are obtained from dynamic ray tracing, the algorithm can readily be incorporated in existing software packages for 3D seismic ray modelling.