A perturbation analysis is presented for calculating the inextensional natural frequencies of curved elastic arcs. Variation of the radius of curvature along the arc length is accounted for by considering the curvature to be a perturbation from a constant curvature, and utilizing the method of strained parameters. Frequencies thus derived for hinged parabolic arcs demonstrate good agreement with finite element solutions. The analysis could easily be extended to determine the natural frequencies of noncircular curved plates and shells.