Abstract: Based on Hamilton's principal, the ordinary differential control equations for the transverse nonlinear free vibration and the buckling of a compressive bar on an elastic foundation are obtained by using the method of "assumed-time-mode". With one end fixed and the other end movable simply supported, the numerical results of the first to third order structural frequencies and the first order buckling load are obtained by employing the shooting method.The results show that the structural frequencies decrease with the increase of the axial compressive force. The structural frequencies and the buckling load increase with the increase of the elastic foundation's stiffness. The effect of the stiffness of the elastic foundation on high order structural frequencies is reduced with the increase of the order number of the vibration modes. The effect of different vibration modes on the first order buckling load is negligible as far as a small amplitude is concerned.