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Recently, a report from Elite Readers suggested that a strange phenomenon of ‘square-shaped waves’ had occurred at the beaches of the Isle of Rhe in the Bay of Biscay. Based on the hydrological and geological data of the Bay of Biscay, we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation. We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev–Petviashvili equation. The combination of exact solutions and actual condition provides the simulated initial state. We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media. Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation. [ABSTRACT FROM AUTHOR]