Vertebrates achieve a high degree of flexibility and skillful performance via a musculoskeletal system consisting of multiple joints. These joints are simultaneously driven by some multi-articular muscles, which run over two or more joints and synchronize the musculoskeletal system. However, when multi-articular muscles contract, buckling may occur in the system if each joint is not adequately supported, such as by monoarticular muscles or intervertebral discs, and we previously investigated the stability conditions for avoiding such buckling by calculating the potential energy of the muscle elasticity. Although in our previous work we considered only the muscles themselves, actual animal muscles are surrounded and constrained by fascia, other muscles, and skin, which may also influence the stability of the musculoskeletal system. Based on this characteristic, in this study, we examined the effect of the surrounding elastic elements that constrain the muscle pathway on the stability of the musculoskeletal system. We analyzed the static stability of the system with respect to potential energy using a muscle path restraint model of the serial link mechanism driven by McKibben-type pneumatic artificial muscles. Moreover, we confirmed the analytical result by conducting an experiment using a six-joint serial link robot driven by antagonistically arranged pneumatic artificial muscles. The results revealed that the restraint of the muscle path influences the stability of the system, and that the support of each joint and restraint is critical for the stability of the system.