The appearance and the structure of the directly-forced waves and cross-waves at the free surface of a fluid contained in a ‘singing wine glass’ are explained by using the superposition method. Cross-waves have crests perpendicular to a vibrating wall, such as in the case of the ‘singing glass’, driven by a moistened finger moving steadily along the rim of the glass. According to experimental studies, the directly-forced waves have four nodes (i.e. are spanning two wavelengths) in the azimuthal direction. For directly-forced waves a linear model could be derived, while for the cross-waves the nonlinear parametric equations are worked out. A graphical representation of the free surface elevation by three eigenmode approximations shows the main features of the wave patterns observed in a singing wine glass.