The predictions of resonance frequencies for elongated elastic cylinders and spheroids, based on various methods of approach, were discussed in a number of papers in recent years. In the present study, the regions of applicability of the phase matching method for surface waves and of the longitudinal bar wave approximation are examined by comparing the predicted results with the results of T-matrix calculations or with the results of scattering experiments. (C) 1997 Acoustical Society of America.