This paper deals with the nonlinear vibrations in an elastic structure which is subjected horizontally or vertically to sinusoidal excitation and to which a liquid container is attached. In theoretical analyses，based on the equations of motion governing the system，the modal equations are derived by taking account of the nonlinearlty due to fluid inertia. The resonance curves are also presented. In numerical calculations，it is found that the shape of the resonance curves changes depending upon the liquid level，and that the liquid container is available as a damping device for structures subjected to horizontal as well as vertical excitation. When the excitation is comparatively large, it is shown that some peculiar vibrations can o㏄ur due to the nonlinearity of the liquid inertia. These theoretical results agreed quantitatively well with the experimental results.