This study presents a general approach to the topology design of tensegrities with rigid bodies. To the best of the authors' knowledge, all existing topology design methods of tensegrities focus on tensegrities that only consist of members carrying axial forces, which are referred to herein as classic tensegrities. However, another category of tensegrities, referred to as general tensegrities, contains rigid bodies aside from axially loaded members. The equilibrium and stability conditions of general tensegrities are different from those of classic tensegrities because of the existence of rigid bodies, which makes the existing topology design methods invalid for general tensegrities. In this study, the equilibrium and stability conditions of general tensegrities are first derived. A topology design approach for general tensegrities is then proposed based on a mixed-integer linear programming optimization scheme. The topology (i.e., member connectivities) is treated as a binary variable, and the member forces are treated as continuous variables. Three essential attributes, namely self-equilibrium, unilateral member force, and class-k condition, of a general tensegrity, as well as some other practical requirements, are formulated as constraints. Different objective functions are employed to design different general tensegrities. Some well-known general tensegrities are reproduced, and various numerical examples are presented to verify the effectiveness and versatility of the proposed approach. The proposed topology design method is verified to be a truly general approach for the topology design of tensegrities with or without rigid bodies. (C) 2020 Elsevier Ltd. All rights reserved.