The resonant sphere technique, RST, has been developed for measurements of elasticity and anelasticity of small crystal specimens. This method has advantages over other methods, especially in high-temperature and high-pressure measurements. New methods of data acquisition have made it convenient to measure resonance frequency at high temperatures (using a buffer rod), making a 1 K temperature interval measurement possible; this opens up many possibilities in the determination of physical properties of solids. Preliminary measurements of resonance frequency were performed by RST up to 100 MPa, which showed interference of vibration modes between the specimen and the pressure medium, even for helium gas as the pressure medium. This interference may become more serious at higher pressures or under liquid pressure. In order to evaluate such effects, the cavity resonance method was developed by Ohno in 1993, with a spherical shell structure with a spherical specimen at the center. This gives clear boundary conditions in the wave equations. Theoretical evaluation of the resonant frequency on such a system shows the necessity of correction to pressure derivatives of elastic moduli, even in measurements up to 100 MPa.