Methods are presented for calculating the laminar boundary-layer flow through separation to reattachment under the influence of a prescribed pressure gradient or, in the case of a supersonic main stream, under the influence of 'free interaction' between the boundary layer and the main flow. The present method is based on the Dorodnitsyn method of integral relations and uses a rational velocity profile which accounts properly for the separation singularity. As a result, the possibility of higher approximations is inherent in the method. The calculated solution for free interaction goes smoothly through the separation point and is in good agreement with certain features of the Navier-Stokes solution in the neighborhood of separation. Good agreement is exhibited between experimental and calculated pressure distributions up to reattachment for the several cases for which the comparisons were made. A computer program based on the work was prepared for two-dimensional flow. It is planned to continue the work to cover nonadiabatic boundary layers and axisymmetric bodies.