The supersonic flow described by the velocity potential for two-dimensional and axisymmetric flows is solved by the finite difference method. This developed method applies to a symmetrical lenticular airfoil, as well as to an axisymmetric body obtained as a result of rotation of the airfoil around its longitudinal axis of symmetry. The problem was solved on the basis of finite differences with the fact that the stabilization of the calculus was carried out by using artificial compressibility. The physical area of the flow is redrawn into the area of calculation so that the swelling corresponding to the contour of the streamlined body is redrawn to a straight line in the area of calculation. The solution method belongs to the class of approximate factorizations of the operator, with the help of which the given flow is described; this is the so-called AF 2 way. Diagrams of the distribution of the pressure coefficient along the contour of the body are provided, as well as a convergence diagram for this example.