The hydrodynamic compliant journal bearings are operating with hydrodynamic lubrication which is generally used to carry radial loads at higher working speed where the standard bearings cannot exist with operation. The both system (journal and bearing) are hold up by a thin lubricating film (fume) due to the distribution of pressure (hydrodynamic). The performance framework prediction of journal bearing, the Reynolds equation (compressible) can be solved by Finite Analysis (FA) method, new Modified Parabolic Approximation and Infinitely Long Approximation. The Modified Parabolic Approximation method converts Reynolds’s equation (classical) into a differential equation which is known as ordinary differential equation. Numerical solutions and a suitable equation are produced for Reynolds’s equation (compressible) using modified parabolic approximation method. The dynamic characteristics study of a gas bearing with this method can be extended which could further help to understand and design of newer generation of journal bearings.