<p>The explicit stiffness of two-layered members and its implementation to the free vibrations of circular arches was studied. The focus lies on two main areas: the explicit stiffness of a structural member with a rectangular cross-section laminated laterally from two different materials is mathematically formulated in terms of axial rigidity, flexural rigidity, mass per unit length, and mass-inertia moment. These stiffnesses formulated were implemented to the free vibrations of circular arches. Governing differential equations with the rotary inertia couple for the free vibrations of arches were derived, followed by numerical solutions to compute the natural frequencies and corresponding mode shapes. The numerical results of this study were tabulated and shown in figures, and the parametric study of natural frequencies is discussed extensively.</p>