An analytic theory of a supersonic flow past a slender profile of an arbitrary shape in the presence of local energy release zones and an external force acting on the flow near the surface is developed. Main results are obtained using the linear approximation, which is valid in a wide range of external conditions. Analytic expressions are derived for calculating the spatial distributions of pressure perturbations near the surfaces of a slender profile at a small angle of attack. The results of analytic calculations are compared with the numerical simulation data based on the Euler equations for a wedge at a zero angle of attack. The comparison reveals good agreement between numerical and analytic calculations. The results make it possible to formulate and solve optimization problems for a supersonic aerodynamic flow with the help of external effects on the supersonic flow.