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Surface waves in crystals are investigated for surface orientations and directions of propagation which preclude waves of plane strain. These waves are of importance in the study of very high frequency vibrations of certain crystal plates. It is shown that, in the AT cut of quartz, one and only one surface wave can propagate along the digonal axis. By reduction to the case of orthorhombic symmetry, it is shown that the surface wave is the result of coupling between a surface wave of plane strain and either a face‐shear mode or a transverse thickness‐shear mode. The former combination is associated with flexural and the latter with extensional vibrations of AT plates. Computation of the wave velocity requires the simultaneous solution of algebraic equations of the third and fifth degrees as opposed to a single cubic equation in the case of waves of plane strain.