The nonlinear vibrations of an elastic structure carrying a liquid-filled cylindrical tank are examined. Modal equations goveming the coupled motions of the structure and liquid sloshing are derived when the structure is subjected to a vertical sinusoidal excitation and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing. This system behaves as an autoparametric system. Then, van der Pol's method is applied to the modal equations to determine the theoretical resonance curves. This demonstrates that the resonance curve for the liquid sloshing changes from a soft spring type to a hard spring type as the liquid level decreases. The structure's resonance curve has a flat shape for an appropriate liquid level. In experiments the theoretical resonance curves were quantitatively in agreement with the experimental results.