Natural frequencies of simply supported elastic arcs vibrating in the plane perpendicular to the plane of initial curvature are obtained by applying a method previously used by the authors to determine upper‐ and lower‐bounds frequencies of curved beams. This method, based on the theory of adjoint operators, was originally proposed by Lehmann, Maehly, and Kato. The centerlines of the arcs are in the forms of circles, cycloids, catenaries, and parabolas. The numerical results obtained are plotted graphically.