Supercritical carbon dioxide (sCO2) power cycles show great potential of higher plant efficiency and power density for a wide range of power generation applications such as fossil fuel power plants, nuclear power production, solar power, and geothermal power generation. sCO2 leakage has been one of the main concerns in such applications. To offer a potential solution, we propose an Elasto-Hydrodynamic (EHD) seal that can work at elevated pressures and temperatures with low leakage and minimal wear. The EHD seal has a very simple, sleeve-like structure, wrapping on the rotor with minimal initial clearance at μm levels. In this work, a proof-of-concept study for the proposed EHD seal was presented by using the simplified Reynolds equation and Lame’s formula the fluid flow in the clearance and for seal deformation, respectively. The set of nonlinear equations was solved by using the conventional Prediction-Correction (PC) method and modern Physics-informed Neural Network (PINN). It was shown that the physics-informed deep learning method provides good computational efficiency in resolving the steep pressure gradient in the clearance with good accuracy. The results showed that the leakage rates increased quadratically with working pressures and reached a steady state at high-pressure values of 15 ∼ 20 MPa., where Q = 300 g/s at 20 MPa for an initial seal clearance of 255 μm. This indicates that the EHD seal could be tailored to become a potential solution to minimize the sCO2 discharge in the sCO2 power plants.