This paper presents measurements of sound velocity and attenuation in olive oil, with known chemical composition, as a function of pressure, within the range of pressure up to 0.7 GPa. Dependencies of sound velocity, relative ultrasonic wave attenuation, volume, and adiabatic compressibility on pressure show discontinuities. This proves the existence of the first order phase transition in olive oil (liquid to solid-like phase transition). Rapid and large changes in relative attenuation testify to the existence of a phase transition in olive oil. Moreover, the kinetics of phase transition was also investigated. Measurement of acoustic wave velocity and relative attenuation in olive oil during the phase transition and in the high-pressure phase is a novelty. The results obtained can be useful in the development of new methods in food (edible oils) control, processing, and preservation.