The last decade has seen clarifications of the underlying capillary physics behind stimulation of oil production by seismic waves and vibrations. Computational studies have prevailed, however, and no viscous hydrodynamic theory of the phenomenon has been proposed. For a body of oil entrapped in a pore channel, viscosity effects are naturally incorporated through a model of two-phase core-annular flow. These effects are significant at the postmobilization stage, when the resistance of capillary forces is overcome and viscosity becomes the only force resisting an oil ganglion's motion. A viscous equation of motion follows, and computational fluid dynamics (CFD) establishes the limits of its applicability. The theory allows inexpensive calculation of important geophysical parameters of reservoir stimulation for given pore geometries, such as the frequency and amplitude of vibrations needed to mobilize the residual oil. The theoretical mobilizing acceleration in seismic waves for a given frequency is accurate to within approximately 30% or better when checked against CFD. The advantages of the viscous theory over the inviscid one are twofold. The former can calculate complete time histories of forced displacement of an oil blob in a pore channel, including retardation by capillary forces, mobilization by vibrations, and an ensuing Haines jump. It also provides an approximately factor-of-two improvement in the calculation of the mobilizing acceleration needed to unplug a static ganglion.