A study of the free vibrations of elastic circular arches is presented, demonstrating the application of a particular direct-iterative eigen-solution method. The model consists of a sequence of straight beam finite elements connecting nodal points lying on the circular elastic axis of the arch. The effect of rotatory inertia is included, but transverse shear deformations are neglected in the analysis. The use of a finite element model facilitates determination of energy distribution in each mode, and permits quantitative analysis of the nature of the frequency spectrum for circular arches of various slenderness ratios. Results also include tables of natural frequencies for circular arches.