A new numerical model based on the level set method is developed for computing unsteady droplet internal flows. The level set is used for capturing and tracking the interface, which is defined as the zero level set of a continuous function. The surface tension is treated as a boundary value condition on the interface, which, through the Young-Laplace equation, determines the pressure jump across the interface. The proposed numerical model is used to simulate oscillation/deformation of an initially elongated neutrally buoyant droplet in an otherwise quiescent fluid under surface tension effects only. Theoretical models for linear droplet oscillation processes are presented and are used to provide a definitive check on the numerical model's accuracy. Nonlinear oscillations are also discussed. Good agreement between theory and numerical simulation is obtained.