Rotating machinery supported on journal bearings is affected by forces due to rotating unbalance and pressure gradients in the oil film. The interaction of these forces can evoke nonlinear behaviour, including asynchronous motion and even chaos. This work attempts to characterise the sub-synchronous motion of the rigid rotor supported on cylindrical journal bearings due to the abovementioned interaction. The analysis focuses on the rotor behaviour at the rotor speeds lower than the threshold speed for oil whirl, associated with sub-synchronous vibration of magnitude equaling the bearing clearance. It is shown that the sub-synchronous vibration can occur well before reaching the threshold speed and that the underlying period-doubling bifurcation depends on the amount of the rotating unbalance. The rotor response and stability are analysed using a numerical continuation method employing the infinitely short journal bearing model. Continuation results are further validated by time simulations which utilise the finite difference method to compute the hydrodynamic forces. The validation process employs bifurcation diagrams, Poincaré sections and numerical estimates of the largest Lyapunov exponents.