The influences of the large amplitude free vibrations of simply supported Timoshenko beams with ends restrained to remain a fixed distance apart and with no axial restraints, which cause a longitudinal elastic force and a longitudinal inertia force, respectively, are investigated. The equations of motion derived by an appropriate linearizarion of the nonlinear strain- displacement relation have nonlinear terms arising from large curvature, longitudinal elastic force and longitudinal inertia force. The fourth order nonlinear partial differential equations for the deflection, can be reduced to the nonlinear ordinary differential equations by means of Galerkin procedure and a modal expansion. The general response and frequensy-amplitude relations are derived by the perturbation method of strained parameters. Comparison with previously published results is made.