Based on the observations in the past earthquake events, the traction elevators in buildings are known to be vulnerable to earthquake induced ground motions. Among several components of an elevator, the counterweight being heaviest is also known to be more susceptible than others. The inertial effects of the counterweight can overstress the guide rails on which it moves. Here we investigate to use the well-known acceleration feedback-based active and semi-active control methods to reduce stresses in the rails. The only way a control action can be applied to a moving counterweight-rail system is through a mass damper placed in the plane of the counterweight. For this, a part of the counterweight mass can be configured as a mass damper attached to a small actuator for an active scheme or to a magneto-rheological damper for a semi-active scheme. A comprehensive numerical study is conducted to evaluate the effectiveness of the proposed configuration of control system. It is observed that the two control schemes are effective in reducing the stress response by about 20 to 25% and improve the system fragility over a good range of seismic intensities.