Summary: The second-order Stokes wave expansion is obtained for flow over a beach of uniform slope with beach angle \(\alpha= (2r- 1)/\pi(2m)\), \(m,r\in\mathbb{N}\). The first-order solution is written as an inverse Mellin transform, and the Van Dyke principle of minimum singularity is invoked at the shoreline, whereby higher-order terms are no more singular than their predecessors. This condition establishes uniqueness at higher orders, and, in particular, for the first-order bounded standing wave we obtain bounded second-order solutions with the presence of a quantifiable radiating second harmonic. This scattered wave is obtained as a finite sum of inverse Mellin transforms for \(r=1\), and is computed for this case. For \(r> 1\), the Melling transform of the velocity potential may be written as a (multiple) integral.