The pressure derivatives of elastic moduli of a steel sphere were measured by the cavity resonance method, a modified resonant sphere technique under gas pressure using a spherical three-layered structure (3LS) consisting of a sample-thin gas layer-cavity container system. The pressure-induced shifts of resonance peaks of both toroidal and spheroidal modes were observed up to 100 MPa (1 kbar) under gas pressure with helium gas. The resultant pressure derivatives of frequencies of toroidal modes yielded a pressure derivative of shear modulus of partial derivativeG/partial derivativeP = 2.01 +/- 0.08. The pressure derivative of the bulk modulus was determined from the data of spheroidal modes, partial derivativeK/partial derivativeP = 5.0 +/- 0.4, by analyzing these data as free oscillations of the 3LS superimposed on the static compression. The results demonstrate the efficiency of the cavity resonance method for measuring pressure derivatives of elastic moduli of solids. (C) 2001 Acoustical Society of America.