Oscillations of oil in a partially saturated porous reservoir are a possible mechanism for the observed spectral modification of ambient seismic background noise above hydrocarbon reservoirs. We couple a 1D wave equation to a linear oscillator equation, which represents the oscillations of the oil within the reservoir. The resulting system of equations is solved numerically with explicit finite differences on a staggered grid in both space and time. The ambient geoseismic noise is simulated by a source term in the equilibrium equations producing a Fourier spectrum of the solid velocity at the surface including all frequencies between 1 and 10 Hz. The numerical simulations show that the oil within the reservoir always oscillates with its eigenfrequency (given a small frictional damping). The corresponding resonance peak is clearly visible in the Fourier spectrum of the fluid velocity. First results show that a smaller Young’s modulus in the reservoir compared to the surrounding elastic material is necessary to transfer the oil oscillations from the fluid to the solid. For this case, the resonance frequency is also visible in the Fourier spectrum of the solid velocity at the Earth surface, because the fluid oscillations are transmitted by the elastic material to the Earth surface.