The motion of an incompressible viscous rotating fluid in an oblate spheroidal container is studied by direct numerical simulation in an appropriate spheroidal coordinate system and in the linear approximation. The behaviour of a few eigenmodes is investigated as a function of the eccentricity $e$ of the container, for Ekman number $E \,{=}\, 10^{- 5}$. Viscous effects are shown through internal shear layers, the spatial structure of which strongly depends on the eccentricity. In particular, for the spin-over mode, a resonance occurs around a critical value $e_c\,{\approx}\,0.50$, where the decay rate deviates strongly from the predicted theoretical variation. This resonance is discussed in relation to the accidental coincidence between the spin-over frequency and two other frequencies corresponding to the (8,1,5) and (14,1,9) inertial eigenmodes.