The present simulation study investigates the effects of ambient pressure oscillation on cylindrical liquid jet sprays, using the volume of fluid method. The research is motivated by combustion instability in combustion engines, where strong harmonic pressure oscillation can damage internal structures. Oscillating pressure modulates not only the fuel mass flow rate but also the ambient gas density and liquid surface tension, and in liquid sprays, the ambient fluid density and surface tension can have substantial effects on spray breakup. In order to investigate the multiple property changes with ambient pressure oscillation, therefore, a new solver in OpenFOAM is developed. In the solver, liquid mass flow rate, ambient gas density, and liquid surface tension change simultaneously as a result of pressure oscillation. Simulations were conducted at a Reynolds number of 2000 and Weber number over 2000, conditions that are conducive to primary breakup in laminar flows. The simulations show that oscillations in ambient pressure significantly strengthen the surface instability of the liquid ligament, which depends on the surface tension–pressure coefficient, the mean pressure, and the amplitude of oscillation.