The resonant sphere technique (RST) is a method of resonant ultrasound spectroscopy developed to measure elastic constants of solids. In this method, resonant frequencies of a spherical specimen are measured and the elastic constants are determined by comparing the measured frequencies with theoretical ones that have been computed for a set of elastic constants. A perfect sphere is not always obtained, however; the specimen sometimes has small asphericity. In this case, the effect of asphericity on the resonant frequencies has to be corrected. Thus a method has been developed to determine simultaneously the elastic constants and asphericity of an aspherical specimen. When RST is employed for elasticity measurements of an ellipsoidal specimen, the difference between measured and computed resonant frequencies is expressed by (delta)(omega)=(phi)[inf i](epsilon)[inf i]+A[inf ij](delta)C[inf ij], where summation convention is assumed for repeated indices, and (epsilon)[inf i] and (delta)C[inf ij] (i,j=x,y,z) are asphericity of the ellipsoid and small corrections for a set of elastic constants, respectively. Since the coefficients (phi)[inf i] and A[inf ij] are known, the unknown coefficients (epsilon)[inf i] and (delta)C[inf ij] can be determined by a least-squares method. Actual application will be reported for an ellipsoid of an olivine specimen with orthorhombic crystal symmetry.