Part III: A finite‐difference method [P. Lloyd and M. Redwood, J. Acoust. Soc. Am.39, 346–361 (1966)] has been used to determine the resonant frequencies and vibration patterns of the first six contour modes of thin rectangular plates ofY‐cut quartz. Predicted resonant frequencies are compared with experimental results for plates of various proportions; in most cases, the difference is less than 1%, even though relatively coarse grids are used in the finite‐difference representation.