Within ICF laser system, many independent laser beams are required to be positioned on target with a very high degree of accuracy during a shot. Optical elements that are capable of moving a laser beam on the target must meet the pointing error budgets. The beam positioning error budgeting was provided. The stability allocation was developed for evaluating the performance of support systems when they were subjected to multiple sources of excitation that can cause motions of optical elements during the alignment procedure and before a shot. The vibrational stability design considerations of support systems on the fundamental frequency, ambient random vibration, and modal damping was discussed. The superstructures of optical elements were the relatively large and massive hybrid structure of reinforced concretes and steel frames or vessels. While the reinforced concrete portions provided optical elements stability, the steel portions afforded design flexibility. Finite element analyses of response of broadband ambient random vibration were performed to evaluate the vibrational stability design of support systems. Measurement on broadband ambient random vibration and beam positioning error in target area of SGIII was described. The measurement result show that its support systems meet the design requirements and these information can be used on similar ICF laser system.