This thesis presents a numerical study of a novel rocking cross-laminated timber (CLT) shear wall system for low- to mid-rise constructions. The system takes advantage of the high in-plane stiffness of CLT coupled with low-yield steel dampers to control the rocking motion of the CLT shear walls during earthquakes. The low-yield steel dampers connected between two rigid CLT wall panels provide the mechanism needed to dissipate the earthquake energy. This concentrates the damage in the dampers, allowing the system to be repaired efficiently after major earthquakes. Numerical models of the CLT shear wall system have been developed using both OpenSees Navigator and ABAQUS software. Models of low-yield steel damper systems were calibrated using available experimental results. With the rigid floor/roof assumption, a simplified OpenSees model of the CLT shear wall system was demonstrated to be effective and reasonably accurate in predicting the response of the system under large excitations. Therefore, it is efficient and reliable to apply the OpenSees model to study the seismic response of CLT shear wall buildings. A case study of a six-storey CLT shear wall building located in Vancouver, Canada was studied; and, detailed parameteric studies were conducted to investigate the influences of the damper type (damper shear strength), number of dampers, damper location, different earthquake records versus target earthquake design response spectrum, and earthquake peak ground acceleration (PGA) on the building response. It was determined that an optimized damper design with comprehensive consideration of these five factors can provide a building with a small roof drift ratio, as well as minor damages on the dampers. Concepts and examples for connection design are also provided.