<p>The mechanism of forced generation and the structure of cross-waves on the free liquid surface in a partially filled cylindrical container have been investigated by the superposition method. For the mathematical description of the cross-waves, single-mode and three-mode nonlinear models have been developed. The single-mode model has described the generation of the cross-waves resulting from the excitation of a resonant mode when the frequency of the cylindrical wall coincides with the corresponding natural frequency. The three-mode model has shown that the cross-waves arise as a superposition of three natural modes, which has enabled an accurate approximation of experimentally observed wave patterns on the free liquid surface. Graphical representations of the free-surface profile obtained with three natural modes have demonstrated the principal features of the wave structures observed near the container wall in the partially filled cylindrical container with a vibrating surface.</p>