The problem of determining the values of the density and elastic constants of an anisotropic body, which provide the minimum, in a sense, sound reflection from a given body, is considered. Statements of both the inverse and the direct problem of the diffraction of acoustic waves from a body – an anisotropic cylinder with a rigid core – in an unlimited space filled with an ideal fluid are presented. An algorithm for solving the inverse problem is described, which is a variation of the genetic algorithm. When using this method, the possible values of the desired parameters of the body are sorted out. The difference between the genetic algorithm and the ordinary enumeration method lies in the use of special operations – “crossings” and “mutations” of parameter sets. For each considered set, called a configuration, a direct problem is solved, in connection with which it is considered in detail in the work. For given parameters of the body and the incident wave, the search for a scattered sound field is based on the model of the propagation of small perturbations in an ideal fluid and the linear theory of elasticity. The general equations of motion of a continuous medium are reduced first to a system of equations in partial derivatives, then to a system of ordinary differential equations. The equations are supplemented with boundary conditions on the surface of the body and on the boundary of the anisotropic part with the rigid core. This makes it possible to determine the expansion coefficients of the scattered wave. The degree of sound reflection is defined as a functional on the space of parameters of the body, expressed in terms of the integral of the potential of the velocities of the scattered wave. Several variants of the functional are proposed, which can be used in various variations of the inverse problem. A genetic algorithm is used to minimize this functional. The paper describes in detail the special parameters of the algorithm and their optimal values, the form of data representation in the genetic algorithm and all the main steps.