The stiffness and frequency properties of tensegrity structures are functions of the pre-stress, topology, configuration, and axial stiffness of the elements. The tensegrity structures considered are tensegrity booms, tensegrity grids, and tensegrity power lines. A study has been carried out on the pre-stress design. It includes (i) finding the most flexible directions for different pre-stress levels, (ii) finding the pre-stress pattern which maximizes the first natural frequency. To find the optimum cross-section areas of the elements for triangular prism and Snelson tensegrity booms, an optimization approach is utilized. A constant mass criterion is considered and the genetic algorithm (GA) is used as the optimization method. The stiffness of the triangular prism and Snelson tensegrity booms are modified by introducing actuators. An optimization approach by means of a GA is employed to find the placement of the actuators and their minimum length variations. The results show that the bending stiffness improves significantly, but still an active tensegrity boom is less stiff than a passive truss boom. The GA shows high accuracy in searching the non-structural space. The tensegrity concept is employed to design a novel transmission power line .A tensegrity prism module is selected as the building block. A complete parametric study is performed to investigate the influence of several parameters such as number of modules and their dimensions on the stiffness and frequency of the structure. A general approach is suggested to design the structure considering wind and ice loads. The designed structure has more than 50 times reduction of the electromagnetic field and acceptable deflections under several loading combinations. A study on the first natural frequencies of Snelson, prisms, Micheletti, Marcus and X-frame based tensegrity booms has been carried out. The result shows that the differences in the first natural frequencies of the truss and tensegrity booms are significant and not due to the number of mechanisms or pre-stress levels. The tensegritybooms of the type Snelson with 2 bars and prism with 3 bars have higher frequencies among tensegrity booms. / <p>QC 20120904</p>