The paper presents algorithms of automatic control of an intelligent anti-tank guided missile (ATGM) with possibility of attacking the target from the upper ceiling and with possibility of the missile flight through indicated points in space. The polynomial functions are used to designate the program trajectories. Numerical analysis of the operation of chosen algorithms is performed. The results are presented in a graphical form. As it results from the conducted tests, the proposed algorithms of automatic control of ATGM with the use of polynomial functions work properly during attack on the target from the upper ceiling, for both mobile and immobile targets.