We have used variational methods based on the work of Holland and Eernisse to predict the resonant frequencies of rectangular resonators for use in acoustic transducer arrays. We have predicted both the open and short circuited resonances and have compared the theoretical results obtained with a large number of experiments carried out on such resonators. When experimentally measured values of the parameters of PZT ceramics are used, the theoretical and experimental results for a wide range of configuration ratios are in excellent agreement, both for the lowest and higher order modes.