The article is devoted to mathematical modeling of flat obstacles punching in Ansys Autodyn software package with the use of finite element method. The tasks of punching flat, composite, two-layer barriers with a drummer at a right angle and 45 degrees angle are considered. With the help of modeling in Ansys Autodyn, the behavior of obstacles is investigated in time and after they are punched by a drummer. In the work, numerical and semi-analytical solutions of the problems were obtained, the results of the solution were presented, comparisons were made and corresponding conclusions were made. A numerical simulation of high-speed collision of barriers with a drummer was carried out, and the rate of through penetration of barriers consisting of several layers was obtained. The layers in the barriers are made up of various materials. The results of numerical simulation of the barrier and the impactor with a conical head are given. © Published under licence by IOP Publishing Ltd.