Dynamic response of a multi-storey symmetrical and asymmetrical space frame structures having six degrees of freedom (three translations along x, y, z-axes and three rotations about these axes) at each node, with multiple tuned mass dampers (MTMD) on its top is obtained. Each tuned mass damper (TMD) is modeled using a two-noded element having two translational degrees of freedom at each node. MTMD with uniformly distributed frequencies is considered for this purpose. The effectiveness of MTMD in suppressing the structural response is determined by comparing the response of corresponding structure without MTMD. It is found that the MTMD can be used effectively to suppress the acceleration, base shear, bending moment, translational and rotational responses of the symmetrical and asymmetrical structures. The effect of important parameters on the effectiveness of the MTMD is also studied. The parameters include the fundamental characteristics of the MTMD such as damping, mass ratio, total number of MTMD, tuning frequency ratio, frequency spacing of the dampers and structural damping. It is shown that these parameters have considerable influence on the effectiveness of the MTMD in reducing the dynamic response of the structure.