<p>Flume experiments play a pivotal role in studying wave propagation, with wave elements typically assumed to remain constant in the perpendicular direction. However, evident cross wave phenomena were observed within flumes under certain conditions. This paper presents new analytical solutions for both primary and cross waves on double shoals in a flume via linear shallow-water equations, which may be used to idealize dynamic experimental configurations of coral reefs. The primary waves on double shoals are described by the associated Legendre functions, whereas the ultimate solutions are derived by considering the incident and reflected waves in front of a bathymetry and the transmitted waves positioned behind it. The effects of the angular frequency and topographic parameters on the primary waves are subsequently analyzed. Cross waves on double shoals constitute a type of topographically trapped wave whose solutions are formulated by combining the first and second types of the associated Legendre functions. The angular frequency is not only determined by the wavenumber but also influenced by the topographic parameters. Numerical experiments are conducted to investigate the generation mechanism of cross waves. The consistency between the numerical results and analytical solutions confirms the validity of the new analytical framework of cross waves on double shoals.</p>