This thesis investigates numerically the phenomenon of flutter in labyrinth seals. Computational fluid dynamics (CFD) methods are used to predict the fluid forces produced in the labyrinth when one of the seal members is vibrating in its natural mode. The geometry of the seal, the vibrational characteristics and the flow characteristics are varied to determine their influence on the aeroelastic stability. The CFD results are used to develop a bulk-flow model for labyrinth seal flutter analysis. An aeroelastic design procedure for labyrinth seal is pro-posed.