The theory of radial vibrations in short, hollow cylinders of barium titanate has been developed. This development results in an expression which relates the radial coupling coefficient to the measurement of the resonant and antiresonant frequencies of the first harmonic of the radial mode of vibration. The important parameter in this development was found to be the ratio of outside diameter to inside diameter, and once this ratio was given, the expression relating coupling coefficient to resonance measurement took a particularly simple form. An interesting result of theory was that for any value of the ratio of diameters, many of the higher harmonics are forbidden in this mode of vibration.Experiments were devised to test some of the theoretical conclusions and were found to be in excellent agreement with the theory.