A uniform force is applied over an arbitrarily orientated bounded plane area in the interior of a semi-infinite incompressible viscous fluid overlain by a dissimilar fluid. Based upon the Papkovitch-Neuber approach to the displacement equations of equilibrium in the theory of elasticity, it is shown that for any orientation of the force and loaded area, the velocities and stresses in the two phases can be found very simply by applying thesame set of differential operators on the corresponding flow fields for a single homogeneous fluid occupying the whole space. A specialization of this theorem admits interpretations in terms of plate bending and extension.