Laboratory experiments have been carried out to study the influence of high-frequency (20 kHz) acoustic waves on the flow of brine through a core sample of reservoir rock containing residual oil. The experiments were done at reservoir conditions with respect to temperature and pressure. Below a certain critical level of the acoustic intensity the relative permeability for the flow of brine is independent of the acoustic intensity and there is no flow of oil out of the core. However, above the critical level the relative permeability for the brine flow jumps to a significantly higher value and oil starts to flow from the core. These experimental results are in agreement with a theoretical model proposed by Graham and Higdon [Oscillatory flow of droplets in capillary tubes Part 2 Constricted tubes. J. Fluid Mech. 425, 55-77 (2000)]. The model is based on a microscopic picture of oil drops (surrounded by flowing brine) being trapped inside the pores of the reservoir rock. Under the influence of ultrasonic waves the oil drops oscillate and can escape from their pores above a critical level of the acoustic intensity.