An investigation was carried out to determine as completely as possible the behavior of a quartz plate vibrating piezo-electrically in modes depending on the thickness. Solutions of the equations of motion were derived and numerical results were obtained giving the resonance frequencies to be expected for any orientation of the plate with respect to the natural axes of quartz crystals;Studies of various edge effects were carried out to prove points predicted by the theory;The filter method of frequency measurement was used in determining the resonance frequencies of the experimental plates.