The development of the composite oscillator method, using nickel transducers, to enable measurement of the rigidity moduli as well as the Young's moduli of small cylindrical specimens is described. The magnitude of the cementing errors for the different modes of excitation is examined both theoretically and experimentally. An analysis is given which shows the advantages, for the technique described, of resonating at the fundamental mode for specimens of relatively low characteristic acoustic impedance. A further consideration of errors due to cross-sectional mismatch between transducer and specimen is made and finally some measurements on coal specimens are given.