In this study, free in-plane and out-of-plane bending vibrations of frame structures have been analyzed together with torsional vibration. Axial extension, rotational inertia and shear effects have also been considered. The frame structure has been constructed as having two beams with doubly symmetric cross-sections and connected at any angle to each other. These types of frames frequently appear on ships as bridge wings which are probably the most problematic members experiencing severe vibration. Internal damping has been incorporated into the analyses by using a complex modulus of elasticity. Natural frequencies have been obtained analytically by solving simultaneous linear equations of complex coefficients. A finite element analysis has also been conducted to verify the analytical results. Furthermore, an experimental modal analysis has been carried out and the results have been compared with theoretical ones in tables for various connection angles and damping factors. The agreement among results has been found to be good.