Exact solution of free in-plane vibrations of circular arches of uniform cross-section is given by considering axial extension, transverse shear and rotatory inertia effects. In contrast with Kirchhoffs beam theory the restrictions of perpendicular cross-section and inextensible are length are removed. The principal axes of the cross-section are assumed to coincide with the principal normal and binormal vectors of the centerline of the beam. A solution procedure is applied to obtain the fundamental matrix for various end conditions. Natural frequencies and mode shapes are given in figures and tables. (C) 1998 Academic Press Limited.