AbstractAdding redundant cables to tensegrity structures is an inevitable requirement for the engineering application of this type of structure. Here we investigated the form-finding and stability of several typical classes of tensegrities with additional cables. An energy minimization–based form-finding method was presented and validated by the analytical solutions developed for prismatic and antiprismatic tensegrities. Some new multistable configurations of typical tensegrities were identified by the proposed algorithm, which demonstrates the robustness of the present form-finding method. It can be revealed from the present analysis that the stability and mechanical properties of the tensegrities with additional cables depended both on the number and the method of adding cables. The stiffness of the antiprismatic tensegrity increased with the increase of the number of additional cables and the reduction of the natural length of the additional cable. But for a more general case, the resistance to deformation of the tensegrity could not always be increased by increasing the number of additional cables. Additional cables could improve the possibility of obtaining more equilibrium states of the tensegrity, but the stability of those equilibrium states was not guaranteed. The transition between two stable self-equilibrated states of a tensegrity could be achieved by just reducing the length of additional cables.