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 designed to have two beams with doubly symmetric cross sections that are connected at various angles to each other. Natural frequencies have been obtained analytically by solving simultaneous linear equations of complex coefficients. Finite element and experimental modal analysis have also been conducted to verify the analytical results. The agreement among the results from the various methods has been found to be good.