Non-linear transient stability analysis has been performed to study the sub-synchronous whirl stability of a rigid rotor supported on two symmetric hydrodynamic bearings with rough surfaces subjected to a unidirectional constant load. A Reynolds type equation for finite hydrodynamic bearings, with different models of rough surfaces, has been solved using the stochastic finite element method. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. Results show an increase in the stability with transverse roughness and a decrease in the stability with isotropic roughness. A small improvement in stability is obtained with longitudinal roughness.