The investigation is a first step to the study of the effect of cross flow in laminar separation at supersonic speeds. It is related to the selection of a final axi-symmetric model. Several problems were examined. First, the effect of streamwise vortices that develop systematically in laminar reattaching flows, triggered by small irregularities in the leading edge thickness. Second, the choice of the diameter of the model such that the flow resembles that of an equivalent planar body, third the programming of Lees-Reeves theory on a 1130 IBM computer to perform a parametric study and finally the development of a new accurate technique or criteria to ascertain that fully laminar shock wave boundary layer interactions can be obtained. (Author).