  We propose a numerical method to compute the inertial modes of a container
with near-spherical geometry based on the fully spectral discretisation of the
angular and radial directions using spherical harmonics and Gegenbauer
polynomial expansion respectively. This allows to solve simultaneously the
Poincare equation and the no penetration condition as an algebraic polynomial
eigenvalue problem. The inertial modes of an exact oblate spheroid are
recovered to machine precision using an appropriate set of spheroidal
coordinates. We show how other boundaries that deviate slightly from a sphere
can be accommodated for with the technique of equivalent spherical boundary and
we demonstrate the convergence properties of this approach for the triaxial
ellipsoid.
