In this paper there are described solutions of the three‐dimensional equations of elasticity and the equations of generalized plane stress pertaining to vibrations of crystal rectangular parallelepipeds and thin plates with traction‐free faces. The modes of motion exist in crystals of certain classes for specific orientations and length‐ratios of the edges. Since the solutions are exact and in closed form, they may be used to advantage in connection with the measurement of elastic constants. Special disposition of electrodes is required for piezoelectric excitation.