The rectangular parallelepiped resonance (RPR) method has proven to be an effective means to measure the adiabatic elastic moduli, C[inf ij], at very high temperatures. The extension of the RPR technique to elevated pressure is an attractive proposition because bonding problems associated with coupling between transducers and specimens are essentially eliminated. However, RPR data have not yet been reported at elevated pressure because of (1) the small frequency shifts observed over the accessible pressure range, and (2) complications in the data reduction scheme by which primary measurements of a resonance spectrum are interpreted in terms of the specimen C[inf ij]'s. The experimental and analysis problems encountered when pressure dependences of modal frequencies are measured will be discussed, and ways in which these problems can be overcome will be presented. A new apparatus in which RPR measurements at elevated pressure have been made will be described. Initial RPR pressure data on several materials will be presented and compared to results obtained when using thermodynamic considerations that relate the temperature dependences of the resonant frequencies to their pressure dependences.