The pore-scale effects of seismic stimulation on two-phase flow are modeled numerically in random 2D grain-pack geometries. Seismic stimulation aims to enhance oil production by sending seismic waves across a reservoir to liberate immobile patches of oil. For seismic amplitudes above a well-defined (analytically expressed) dimensionless criterion, the force perturbation associated with the waves indeed can liberate oil trapped on capillary barriers and get it flowing again under the background pressure gradient. Subsequent coalescence of the freed oil droplets acts to enhance oil movement further because longer bubbles overcome capillary barriers more efficiently than shorter bubbles do. Poroelasticity theory defines the effective force that a seismic wave adds to the background fluid-pressure gradient. The lattice-Boltzmann model in two dimensions is used to perform pore-scale numerical simulations. Dimensionless numbers (groups of material and force parameters) involved in seismic stimulation were defined carefully so that numerical simulations could be applied to field-scale conditions. Using defined analytical criteria, there is a significant range of reservoir conditions over which seismic stimulation can be expected to enhance oil production.