In this paper an extension of the theoretical model of Molin (J. Fluid Mech., vol. 430, 2001, pp. 27–50) is proposed, where the assumptions of infinite depth and infinite horizontal extent of the support are released. The fluid domain is decomposed into two subdomains: the moonpool (or the gap) and a lower subdomain bounded by the seafloor and by an outer cylinder where the linearized velocity potential is assumed to be nil. Eigenfunction expansions are used to describe the velocity potential in both subdomains. Garrett’s method is then applied to match the velocity potentials at the common boundary and an eigenvalue problem is formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Applications are made, first in the case of a circular moonpool, then in the rectangular gap and moonpool cases. Based on so-called single-mode approximations, simple formulas are proposed that give the resonant frequencies.