Ray tracing is a simple and efficient three-dimensional method which reduces the problem of infrasound propagation to a series of one-dimensional cases along acoustical rays. However, in relatively frequent cases, infrasound stations are located in geometrical shadow zones, where only diffracted waves are recorded. The corresponding arrivals cannot be predicted by ray theory. To simulate infrasound propagation in these zones, the ray tracing method is generalized to complex ray theory. The source, media, and ground parameters are all considered as complex numbers. For applications with realistic atmospheric data, including stratified temperature and wind as well as the range dependency of atmospheric profiles, an efficient algorithm determining complex eigenrays in the shadow zones is presented. It is illustrated by a two-dimensional case of a point source.