AbstractThe shape of the free surface and the flow field of a simple fluid driven by the steadily rotating bottom cap of a cylindrical cup is investigated. A regular domain perturbation in terms of the angular velocity of the bottom cap is used. The velocity field is a superposition of a strong primary, azimuthal field and a weaker secondary meridional field. The effect of the aspect ratio and viscoelasticity of the fluid results in multiple cell structures in the meridional plane. The free surface shape determined at the lowest significant order in the perturbation algorithm, is similarly affected by the same factors. Both the flow field and the interface shape are determined for a wide range of aspect ratios and viscoelastic parameters.