A variational principle is used to develop an approximate analytical method for the evaluation of the nondivergent normal modes of a rotating closed basin with topography. As an example, the effects of a continential shelf, a mid-ocean ridge, and a seamount on the modes of an otherwise flat basin are studied. The dependence of the frequency of the higher modes on the parameters of the problem is shown; in particular, emphasis is given to the relative importance of the width and height of the topography and the gradient of planetary vorticity β. A suitable parameter to measure the relative weight of both effects is &tgr;=FF F2(ϑ ln h)2d&Lgr;/FFβ2 dA, where h is the depth, F is the Coriolis parameter, and the integration is carried over the whole basin. In the three cases studied, topographic effects are important for the fundamental mode for values of &tgr; larger than 0.25/Δ, for a square basin with a shelf or a ridge of relative width Δ, and &tgr; ~0.5 for a circular basin with a seamount. When the topography is important, large departures from the flat bottom case are found for both the structure and the frequency of the modes. Longuet-Higgins showed that for a constant depth the modes extended over the whole basin. The frequency of the gravest mode is approximately ω=βL/2&pgr;, where the length scale L is of the order of the dimensions of the basin: higher modes have larger periods with an accumulation point at zero frequency. In the cases studied above the modes tend to be trapped over the topographic features as &tgr; increases, and thus the length scale is reduced to something of the order of the width of the topography. But on the other hand, the effective value of β is considerably increased to the magnitude of h∇ (F/h) in the trapping region. The net result is an increase of the eigenfrequencies. The results are compared with those of numerical models, and approximate formulae, valid for strong topography, are developed for the shelf and ridge cases.