When the free surface is anisotropic, mode of elastic surface‐wave propagation can arise that has many of the properties of a normal surface wave but has a phase velocity higher than that of the transverse bulk waves in the corresponding direction. The pseudo surface wave is a coupled mode involving terms decaying rapidly beneath the free surface and a term representing a bulk wave radiating into the solid. For many choices of crystal and plane of propagation, the contribution of the bulk term over a range of directions is small enough that the energy of the wave is essentially concentrated within a few wavelengths of the free surface and flows parallel to the surface as with the normal elastic surface waves. Moreover, in certain specific directions, the bulk term disappears completely and the pseudo‐surface wave has all the properties of a normal surface wave. The method of computation of the characteristics of the pseudo surface waves is outlined here and typical results of velocity, displacements and energy flow are given for an assortment of anisotropic crystals and planes of propagation.