Since ultrasonic velocities in anisotropic media can change by a factor of 3 or more depending on the direction of propagation, accounting for these changes is extremely important. Also many anisotropic materials are made up of multiple layers of varying orientation, hence the need to account for refraction at ply boundaries. In the present invention, an algorithm is used to calculate these velocities and travel times and properly account for refraction phenomena. Specifically a multilayer SAFT algorithm has been developed that will calculate the time shift, shift and sum A-scan waveforms in layered anisotropic media at any given depth, ply orientation, and number of plies. The algorithm showed an improvement in signal to noise ratio with synthetic data as was expected. This algorithm can be used as a replacement for homogenizing material properties in layered media and will calculate time shifts with increased accuracy since exact material properties are used.