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Microwave pulse-echo experiments have been performed using YIG samples, and data are presented illustrating a variety of elastic, magnetoelasfic, and spin wave propagation phenomena. Both disks and rods of YIG were used, with excitation at X-band frequencies. The spin wave mode of propagation shows very strongly dispersive behavior when the spin wavelength is comparable to one of the sample dimensions. The group velocity is obtained from the magnetostatic mode spectrum of the appropriate configuration and is combined with the spatial variation of the internal magnetic field to compute the delay time. Exchange effects are important in the case of the disk and are included in the analysis. The agreement between theoretical and experimental delay times is quite satisfactory for all configuration.