A liquid droplet may go through shape oscillation if it is forced out of its equilibrium spherical shape, while gas bubbles undergo both shape and volume oscillations because they are compressible. This can happen when droplets and bubbles are exposed to an external flow or an external force. Liquid droplet oscillation is observed during the atomization process when a liquid ligament is first separated from a larger mass or when two droplets are collided. Droplet oscillations may change the rate of heat and mass transport. Bubble oscillations are important in cavitation problems, effervescent atomizers and flash atomization where large number of bubbles oscillate and interact with each other. This chapter provides the basic theory for the oscillation of liquid droplet and gas bubbles.