Gas-discharge lamp and electrostatic antenna are important elements of the system of permanent light marking of 35–110 kV overhead power lines. The paper considers the possibility of using electrostatic antennas of irregular shape to increase the luminous intensity of gas-discharge lamps. It is shown that the frame antennas under the conditions of limiting the maximum size allow higher operating current and brightness of the gas-discharge lamp than in case of a standard rectilinear antenna. To estimate the electrical capacity of the irregularly shaped antennas made of a thin circular cross-section profile, the authors applied the method of an integral equation of the first kind with respect to the distribution of the linear charge density on the structural elements. Using the COMSOL Compiler and MATLAB Compiler tools, the authors developed application software, which allows geometric parameters input, antenna design visualization, and calculation of the electrical capacitance. The spatial displacements of irregularly shaped antennas under the influence of wind loads are estimated.