The general solution of ultrasonic wave scattering by an elastic sphere embedded in solid matrix with an interface layer is developed. A transfer matrix connecting the displacement and stress components on the opposite surfaces of the layer is derived. Asymptotically expanding the transfer matrix gives the equivalent boundary conditions at an interface. A spring model for describing physically a spherical imperfect interface is thus established and its validity is evaluated. Ultrasonic scatterings respectively from rigid and slip interface are numerically compared.