Journal bearings have many applications in industry due to its high load carrying capacity. In addition proper design of journal bearings enables safe operation at very high speeds. However, they are susceptible to oil whirl instability which may cause bearing failure. The fluid film pressure distribution inside the journal bearing is described by Reynolds equation. Many studies had been done to approximate the bearing performance using first order bearing coefficients. Although this analysis is stable for evaluating the threshold speed but it is insensitive to limit cycles above the threshold speed. Mush literature show that above the threshold speed, subcritical or supercritical bifurcations may be observed. Therefore, the aim of the present paper is to evaluate the third order bearing coefficients for a finite length journal bearing using finite perturbation method. The values of these coefficients are evaluated using infinitesimal perturbation analysis. These values are used to investigate the bifurcation stability of flexible Jeffcott rotor supported by two symmetric journal bearings. The effect of rotor stiffness ratio on the bifurcation stability of the system is investigated. The results of this work show that the third order parameters can be used to evaluate the type of bifurcation above the threshold speed.