A representative formulation of the one strip blunt body integral method is treated in sufficient detail to delineate the numerical difficulties involved in its mechanization as well as to identify limitations in its application. While the integration of the governing system of equations for general body shapes comprises a two-point boundary value problem, the particular case of a flat-faced cylinder is shown to reduce to a procedure involving a single integration. An investigation is made of the extent to which conservation laws are satisfied throughout the shock layer region. Significant deviations are found to exist depending upon the method used for computing the distribution of flow properties across the shock layer. A procedure has been chosen which insures compatible tangential and normal flow property gradients at the shock and body while significantly reducing mass and momentum defects in most instances. Computed flow field data are presented for spheres and flat-faced cylinders.