So-called ‘moonpools’ are vertical openings through the deck and hull of ships or barges, used for marine and offshore operations, such as pipe laying or recovery of divers. In the present study rectangular moonpools of large horizontal dimensions are considered. The natural modes of oscillation of the inner free surfaces are determined, under the assumption of infinite water depth and infinite length and beam of the barges that contain the moonpools. The problem is treated in two and three dimensions, via linearized potential flow theory. Results are given for the natural frequencies and the associated shapes of the free surface, for wide ranges of the geometric parameters. Simple quasi-analytical approximations are derived that yield the natural frequencies. The most striking result is that the natural frequencies of the longitudinal sloshing modes increase without bounds when both the draught and the width decrease to zero, the length of the moonpool being kept constant. As a corollary the problem of waves travelling in a channel through a rigid ice sheet is addressed and their dispersion equation is derived. The same behaviour is obtained: the waves travel increasingly faster as both the draught and the width of the channel are reduced.