Wave propagation in layered media is a fundamental topic in underwater acoustics. Several computational methods have been developed and used. Here, we apply the Riccati method, involving recursive computation of reflection and transmission matrices, and the finite differce method. We consider the extension when the layers are allowed to contain periodic arrays of scatterers. With the Riccati method, multiple scattering from the cavities is handled by adapting techniques developed for electron scattering and recent applications to band gap computations for photonic and phononic crystals. With the finite difference method, multiple scattering from the cavities is handled automatically by incorporating periodic boundary conditions for a unit cell. As an application, we model the performance of Alberich anechoic coatings. Rubber layers with cavities are used to redistribute normally incident sonar energy in the transverse direction, where it suffers losses by anelastic attenuation.Useful forward modelling tools are obtained, which allow evaluation of the anechoic effect of coatings involving different kinds of cavities. Global optimization techniques are used to design coatings with favourable anechoic performance over broad frequency bands. In one exemple, an echo reduction of 18 dB or more is achieved within the frequency band 15-30 kHz.