The length extensional vibration mode of a piezoelectric ceramic substrate is used in fabricating the ultra-small size resonators and filters. In general, the three side ratios of the rectangular substrate affect the resonant characteristics of the resonator using its length extensional vibration. In this paper, their relationships are studied. We know that changing the ratio of its length to its width makes possible to change the resonant frequency of the width vibration without degrading the length extensional vibration. And frequency constant for length extensional vibration becomes slightly small as the substrate thickness becomes thin, but it does not change as its length changes. Electro-mechanical coupling factor for length extensional vibration, k$\_$31/ does not change as its length changes within length/width$geq$4, but it becomes small as its width increases.