Labyrinth seals are widely used in various turbo machines including turbines, compressors and pumps. Their purpose is to prevent the backflow of the working fluid. This backflow is due to the leakage of the seal. This loss affects the efficiency of the turbo machine, so it becomes critically important to assess the leakage of the seals under the given operating conditions. The accuracy of prediction of leakage is also important for performing rotodynamic analysis. The geometric shape of the seal plays an important role in influencing the fluid flowing through the seals and the leakage rate. Many empirical seal leakage prediction models, useful from a design/analysis point of view, have been developed. Saikishan Suryanarayanan and Gerald. L .Morrison studied the influence of various geometric and flow parameters on the leakage of labyrinth seals with rectangular cavities. They proposed a leakage equation based on their Computational Fluid Dynamics (CFD) simulations using software FLUENT. However, many real world labyrinth seals do not have simple rectangular cavities. In particular, this thesis focuses on seals with Isosceles triangle shaped teeth, right triangle shaped teeth, and a NASA seal. In the present work, CFD simulations of labyrinth seals with advanced cavity shapes are performed and the results are compared with the predictions of the rectangular seal model. The results show that the advanced cavities like, Isosceles shaped seal were more efficient as compared to rectangular seals. The pressure drop, which was taken as one of the key parameters to adjudge the efficiency of seals showed negative behavior in some of the advanced cavity shaped seal. The advanced cavity shaped seals are used in various turbo machinery equipments like steam and gas turbines. This study shows that Isosceles cavity shaped seals are the most efficient among all the advanced cavity shapes used in the present study.