Abstract: The sound fields inside and outside a cylindrical layered structure with transversely isotropic symmetry due to an obliquely incident wave are described in the paper. By using the transfer matrix approach, the linear algebraic equations in matrix form are derived to determine the potential functions of the scattered waves. Some namerical computations are made for the backscattering spectra and scattering cross-sections. A spring model for simulating an anisotropic interphase layer between, for example, a fiber core and isotropic matrix medium is developed. The generalized boundary conditions at an interphase are also given. The results indicate that the spring stiffnesses in the obtained spring model depend on the layer thickness and the elastic constants c₁₁, c₁₂ and c₄₄, while their mass terms are related with c₁₁, c₄₄, c₁₃ and c₃₃.