In rotating machinery, rubbing occurs between the rotor and the stator, at the seal, between the rotor and the guide and between the rotor and the backup bearing. The backward rub or the partial impact vibration can be avoided by lubricating the contact surface sufficiently in order to decrease the friction. However, forward rub may still occur in such a case with a lubricated contact surface. Once such a forward rub occurs, it remains even if the rotational speed increases to much larger than the first bending critical speed and it is difficult to escape from this forward rubbing condition automatically. This paper proposes the suppression method of this forward rub by introducing the directional difference in the support stiffness of the guide or the backup bearing. The nonlinear theoretical analysis clarifies and explains the usefulness of the proposed method and it is also validated experimentally.