Axisymmetric supersonic flow about a thin body of revolution with an external energy supply and an external force localized near the body surface is considered in the linear approximation. An analytic theory is constructed for calculating spatial fields of flow parameters in this case for an arbitrary dependence of external effects on the longitudinal coordinate. Formulas are derived for the pressure ratio on the surface of the thin body of revolution. The results of calculations based on the analytic theory are in good agreement with numerical data obtained from the solution of hydrodynamic equations in the Euler approximation.