Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements providing opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, replacing sequences of cable elements by continuous cables sliding over joints significantly changes the mechanics of classical tensegrity structures. Furthermore, challenges emerge for structural analysis, control and actuation. In this paper a modified dynamic relaxation (mDR) algorithm is employed to investigate actuated tensegrity structures with continuous cables. The dynamic behavior of such structures is also investigated.