Mechanical modelling and associated numerical methods are able to improve the design of absorbing materials which are otherwise difficult to accomplish through experimental studies only. In this paper, we provide an original procedure for obtaining high acoustic absorption of single and multi-layered panels with predefined microstructure. The procedure uses the homogenisation technique for obtaining effective properties of an airsaturated material and solution to acoustic problems. We study a certain topology of the material and point out the effect of matrix material stiffness on the results of the optimisation procedure. We demonstrate that for stiff and rigid frames of a single layer, the optimal design parameters do not differ much whereas for the soft frames, the same results may significantly change. Moreover, we show that the absorption properties can be essentially improved by arrangements of different materials (soft, stiff and air) in sandwich panels. It is also possible to design a material which efficiently absorbs acoustic energy at low frequencies which is hard to achieve by means of conventional materials.