The main objective of the present work is to develop an algorithm consisting of the eigenvalue sensitivity and modal updating along with the mode tracking to analyze the dynamic behavior (i.e., vibrational properties) of a tensegrity structure. The optimum values of the design parameters including the pre-tension force, element section area, etc., are obtained to satisfy the desired vibrational properties of the structure. The optimum variables will be acceptable if the design constraints involving the buckling constraint for rod elements and the strength constraints for all components of the system are fully satisfied. The efficiency of the proposed algorithm for finding the optimum values of the design variables of the tensegrity structures is proved through the solution of three examples