In this paper is discussed the way of suitable numerical solution of contact shape optimization problem. The first part of the paper is focused on method of global optimization field among which the genetic algorithm is chosen for computer processing and for application on contact problem optimization. The brief description of this method is done with emphasis of its characteristic features. The experiment performed on plane structural problem validates the ability of genetic algorithm in search the area of the global optimum. On the base of the research described in this work, it is possible to recommend optimization technique of genetic algorithm to use for shape optimization of engineering contact problems in which it is possible for any shape to achieve successful convergence of contact task solution.