In this study the modal characteristics and responses of an asymmetric structure with added viscoelastic dampers were investigated for design parameters such as eccentricity of stiffness and added dampers, the loss factor of the damping materials used. For modal characteristics, variation of the quantities such as natural frequencies, modal damping ratios, modal participation factors, and dynamic amplification factors were observed, and displacements at flexible and stiff edges, and at center of mass were obtained. Based on the results, the problem of the optimum damper distribution to minimize the torsional effects was addressed, and the proposed method for optimum damper distribution was applied to a multi-story structure to verify the applicability Finally the effect of viscous and viscoelastic dampers were compared by varying the loss factor of the viscoelastic material.