This paper presents an original method for the analytical computation of a non-rectangular patch antenna input impedance, with more or less regular shapes (polygon, trapezoid…). The method is based on a modal analysis of the equivalent cavity. Based upon classical patch impedance equations deduced from the transmission line model (circuit model), the modal analysis (cavity model) allows the extension of these equations to other shapes by replacing the length and the width by their equivalent dimensions in the involved shapes. The method is illustrated by a regular hexagonal patch antenna. Explicit equations are proposed and validated through comparison between simulations and measurements.