The general equation for determining the scattered sound wave coefficients by an elastic cylinder encased in solid matrix is derived.A thin interphase layer between the matrix and cylinder is taken into account.The resonance modes and related eigenfrequencies in the backscattering spectra are discerned based on the Flax's theory.By using the spring model for interphase layer,the effect of the shear stiffness constant KT on the resonance scattering modes is evaluated.