Free surface flow in a cylindrical container with steadily rotating bottom cap is investigated. A regular domain perturbation in terms of the angular velocity of the bottom is used. The flow field is made up of the superposition of azimuthal and meridional fields. The meridional field is solved both by biorthogonal series and a numerical algorithm. The free surface on the liquid is determined at the lowest significant order. The aspect ratio of the cylinder may generate a multiple cell structure in the meridional plane which in turn shapes the free surface.