This paper discusses the use of the authors’ fast methods and programs for the calculation of 3D supersonic flow about a flying vehicle and thermogas dynamic processes in the components of an airframe-integrated ramjet. To conduct fast comprehensive calculations, use is made of marching methods, which are two to three orders of magnitude faster than pseudoviscosity methods. 3D supersonic flows about the airframe, in the inlet section of the air intake, and in the exhaust jet are calculated using a “viscous layer” model or Godunov’s scheme for the inviscid approximation. Subsonic flows in the outlet section of the air intake and in the combustion chamber are calculated using a “narrow channel” or a quasi-one-dimensional model. The elements of the presented methods and programs that complement a previously proposed fast comprehensive model are described in more detail. A method for assigning the spatial shape of the flying vehicle surface and the ramjet duct walls is described. A simplified approach to determining the critical area of the exit nozzle in the one-dimensional approximation is proposed. The paper substantiates the advantages of marching methods over pseudoviscosity ones in the predesigning of ramjets with direct account for flow choking, which may occur in the combustion chamber or the exit nozzle. The calculated 3D flows in the individual components and the full assembly of a stylized-shape flying vehicle are presented. The main advantages of the proposed methods and programs are their comprehensiveness and fast computation speed. Their use in the calculation of 3D supersonic flow about a ramjet flying vehicle shortens the ramjet component predesigning time.