Under the assumption of a perfect gas with a constant specific heat ratio, the first approximation of the integral-relations method, which considers the entire shock layer as a single strip, is derived for axisymmetric bodies of arbitrary smooth contour. The resulting differential equations were then applied to a supersonic and hypersonic flow past a paraboloid of revolution. The shock shapes, shock wave detachment distances, locations of sonic lines; and velocity and pressure distributions for the body were calculated for γ = 1.4 and y = 5/3, and at Mach numbers of 3, 4, 6, 10 and 1000. These calculations were carried out on an IBM 1620 electronic computer. The results were compared with those obtained by Van Dyke's inverse method. The agreement between the two methods was found to be good, in view of the fact that only the first approximation of the integral relations method was used. / Master of Science