Simple analytical solutions are presented for nondivergent topographic waves (rotational modes) in a certain type of elliptical basin. Under the assumption that the basin's depth contours form a family of confocal ellipses, the governing potential vorticity equation in elliptic cylindrical coordinates reduces to a Cartesian form, independent of the coordinate scale factors. As a consequence, for the exponential depth profileh=e−bξ, where ξ is the radial coordinate, the radial eigenfunctions for elliptically travelling waves in a basin with a partial vertical barrier along the centerline can be expressed in terms of elementary functions. For a lake without a barrier, approximate analytical solutions are obtained by the Rayleigh-Ritz (variational) method. The periods and streamline patterns of the first few modes of the variational solutions are compared with those due to Ball (1965) for an elliptic paraboloid.