A general formulation of an inverse problem of structural mechanics as an optimization problem is presented. The following features of a typical problem are accentuated: a large computational effort needed to evaluate the function values multiplied by the number of calls for the numerical simulation of the process under consideration, and that the function values often present some level of numerical noise. The main features of the Multipoint Approximation technique based on the Response Surface methodology (MARS) are presented with the emphasis on the choice of approximation functions. As a promising way of selection of the structure of approximations, the Genetic Programming methodology is presented. The use of optimization techniques for the solution of inverse problems of structural mechanics is illustrated by examples of damage recognition in steel structures and identification of parameters in various constitutive models.