Аннотация:The problem of determining the acoustic field in a metamaterial can be divided into two steps in many cases. First, the scattering matrices of the individual metamaterial elements are calculated. Second, they are used to solve the direct scattering problem and to determine the desired field. Since the metamaterial elements are small, the scattering matrices can often be reduced to just a few scattering coefficients, which makes the solution computationally efficient. The advantages and limitations of this approach are discussed. The task of designing the elements of a metamaterial with the given properties is posed. Two methods of its solution are proposed: based on the functional Novikov algorithm and by selecting the geometric and physical parameters of the metamaterial elements models. The results of several numerical simulations are presented.