Gas bearings are extensively used in several industrial applications to support the rotating load at high speed due to its favorable characteristics. The numerical computation of the gas film damping and stiffness coefficients is a difficult task due to nonlinearity in the Reynolds equation for compressible lubricant. In the present work, a numerical method based on the finite element method is developed for the direct computation of gas film damping and stiffness coefficients. In this method, a double partial differential equation approach has been used to compute the dynamic characteristics. Further, the numerical results presented shows that the bearing ellipticity ratio significantly affects the nonlinear trajectory of the journal. © 2017, © IMechE 2017.