The generalized ray, combined with the system matrix, can be utilized to calculate the travel time of the elastic waves in stratified anisotropic media. The method proposed by Van der Hijden is modified to calculate the horizontal slowness (corresponding to travel time) of the Cagniard path. The accuracy of this method is verified by comparing the results with those of perturbation and ray tracing methods. ¿ American Geophysical Union 1995.