Elastic wave-based enhanced oil recovery (EOR) is being investigated as a possible EOR method, since strong wave motions within an oil reservoir - induced by earthquakes or artificially generated vibrations - have been reported to improve the production rate of remaining oil from existing oil fields. To date, there are few theoretical studies on estimating how much bypassed oil within an oil reservoir could be mobilized by such vibrational stimulation. To fill this gap, this paper presents a numerical method to estimate the extent to which the bypassed oil is mobilized from low to high permeability reservoir areas, within a heterogeneous reservoir, via wave-induced cross-flow oscillation at the interface between the two reservoir permeability areas. This work uses the finite element method to numerically obtain the pore fluid wave motion within a one-dimensional fluid-saturated porous permeable elastic solid medium embedded in a non-permeable elastic semi-infinite solid. To estimate the net volume of mobilized oil from the low to the high permeability area, a fluid flow hysteresis hypothesis is adopted to describe the behavior at the interface between the two areas. Accordingly, the fluid that is moving from the low to the high permeability areas is assumed to transport a larger volume of oil than the fluid moving in the opposite direction. The numerical experiments were conducted by using a prototype heterogeneous oil reservoir model, subjected to ground surface dynamic loading operating at low frequencies (1 to 50 Hz). The numerical results show that a sizeable amount of oil could be mobilized via the elastic wave stimulation. It is observed that certain wave frequencies are more effective than others in mobilizing the remaining oil. We remark that these amplification frequencies depend on the formation’s elastic properties. This numerical work shows that the wave-based mobilization of the bypassed oil in a heterogeneous oil reservoir is feasible, especially when combined with another EOR method, such as wettability alteration by low-concentration surfactant injection. The extension of this research into a more realistic three-dimensional reservoir model would help determine the optimal locations and frequencies of wave sources that could maximize the volume of mobilized oil.