A set of differential force and moment equilibrium equations for the in‐plane dynamic strains in an oval ring of variable thickness is determined. This set is reduced to algebraic form by substituting Fourier series for the stresses and deformations. The resulting matrix is then truncated and evaluated in order to determine the first five normal modes and the first eight natural frequencies for an elliptical ring of uniform wall thickness. Excellent agreement is shown between theoretical and experimental data for several aluminum rings of pseudoelliptical shape.