It is known that the presence of a small inhomogeneity in a uniform supersonic flow can lead to the global restructuring of the flow around bodies. An aerodynamic wake behind a solid particle [1] or a thermal wake from a source of external power supply [2] are typical examples of the formation of a localized inhomogeneity in the supersonic flow. 1 One of the brilliant manifestations of the capability of the small inhomogeneity to induce the global restructuring of the flow is the formation of a large separation region formed in the supersonic flow in front of a blunt body; this region displaces the bow shock wave far ahead with a simultaneous sharp decrease in the wave drag of the body [3]. Such a phenomenon is observed in many physical [4, 5] and computational [6‐9] experiments. The idea to affect the structure of gas flows by means of artificial inhomogeneity sources (e.g., solid particles, pellets, thrown to the supersonic counter flow [1, 10, 11] or “spots” of intense heat supply that are created in the flow in front of the body by means of various electric or laser optic discharges [4], etc.) has been considered by many researchers as a new method for controlling the aerodynamic characteristics of promising aircraft [13]. Configurations of flows with global separation induced by the small inhomogeneity are similar to an example of the nonunique solution of the problem on the supersonic flow around bodies that is known in the gas-dynamics course [14]: in a uniform supersonic flow in front of a round cylindrical body, a conical region of immobile gas can exist, which is separated from the external flow by the tangential discontinuity surface (see Fig. 1). Since various pressure values can exist in 1 There is no fundamental difference between these two variants of the inhomogeneity, because the dynamic component of the inhomogeneity is determining in both cases [10, 12]. this dead zone, there are an infinite number of conical configurations of the dead zone in front of the body. The selection of one of them is impossible without additional information on the causes of the separation of the flow from the body [14]. In this work, the problem of the selection of a single solution is analyzed for the case where the cause of the appearance of a large separation region is a small inhomogeneity in the incident supersonic flow. It is shown that an inviscid steady flow with an isobaric dead zone exists under certain conditions. This flow in the local inhomogeneity scale is a flow with a separated compression shock and, upon transition to the external global scale, is continuously transformed to a self-similar supersonic flow with a thin entropy layer at the boundary of the dead zone, where the pressure is equal to the total pressure p 01 behind the normal shock in the inhomogeneity core. The parameter p 01 selects a single configuration with the conical dead zone in front of the body. The corresponding flow is a