The parameters of a conical stabilizer and its effect on the aerodynamic characteristics of the high-speed air vehicle, in general, are examined. The flow characteristics of an high-speed air vehicle with a conical stabilizing device are analyzed. Simulation results are compared with experimental data. Qualitative features of the supersonic flow associated with the characteristics of the drag of an aerodynamic configuration with a stabilizing device in the form of a truncated cone are considered. Particular attention is paid to the physical aspects of the flow around the considered configurations and to elucidating the mechanisms responsible for a minimum in the drag coefficient of a wingless high-speed air vehicle. A general mechanism of occurrence of the minimum in the drag coefficient for aerodynamic configurations with a conical tail stabilizer is studied.