We present a new approach to analysis of curvilinear perfect conducting surface radiators. The feature of this approach is a formulation of boundary value problem as a system of integral equations in regard to the complex electrodynamic vector potential and the scalar potential and simultaneous solution of this system for unknown distributions of current density vector and charge density using technique of parametrical mapping for representing curvilinear surface and the Galerkin’s method with boundary elements. Advantages of the approach in comparison with the Harrington integral equation on example of surface current distributions at the third order surface (Ferguson’spatches) are demonstrated.