Today, both the government and private aircraft companies strive for faster, lighter, and less expensive aircraft to stay competitive in both the national and international arena. This is only possible with continuous innovation and sustainability efforts for aircraft systems such as fans, compressors, combustors, and turbines, as well as the sub-systems including engine seals. Advanced engine seals show significant promise for improving the engine pressure ratio and cycle temperatures, which result in lower engine weight, stronger thrust, and higher fuel efficiency. We propose an innovative multistage seal concept that leverages the well-known Elastohydrodynamic (EHD) lubrication theory. In this study, a physics-based computer simulation modeling approach was employed. Due to the highly non-linear nature of the complex Fluid-Solid-Interactions (FSI) between the seal and the rotor, a fully coupled Finite Element Analysis (FEA)-Computational Fluid Dynamics (CFD) based modeling was adopted for the design of the seal system. With the recent improvements in the commercially available software, COMSOL Multiphysics software was employed to carry out the fully coupled FSI simulations. The modeling approach was presented thoroughly, and the results were discussed. The leakage was found to be less than 0.010 kg/s at 2.75 MPa. The proposed seal system could be an alternative to the existing sealing technologies in the market.