A one-fluid model of viscous interaction between the shocked solar wind flow in the Venusian ionosheath and the ionospheric plasma is formulated through a conventional MHD viscous boundary layer theory. The geometry considered applies to the flank regions of the ionosheath, exterior to the ionospheric cavity. Adoption of the proper boundary conditions for this problem leads to velocity profiles which support the interpretation of the Venusian ionopause in terms of a thick mixing region which is gradually forced to taper toward the axis of the ionospheric cavity, as can be inferred from the Mariner 5 and Venera 4 data.