The energy method has been used to derive the governing equations of motion for transverse vibrations of curved sandwich beams. Assuming a series solution, the equations are solved for a simply supported curved sandwich beam with viscoelastic cores. The damping effectiveness of the beam is evaluated by application of the correspondence principle of linear viscoelasticity. Theoretical results for resonant frequencies and associated system loss factor for curved sandwich beams have been verified experimentally. The effects of curvature, core thickness, lack of symmetry and modal number on the resonant frequency parameter and associated system loss factor have been studied.