The vibration is a main factor to influence the performance of chain drive. The difference between normal roller chains and constrained conveyor chains is that the main vibration mode of constrained trajectory conveyor chains is longitudinal. The model and its equivalent model are established to solve this problem.The kinetics model is built to resolve the natural frequency and principal mode based on the vibration theory of multiple-degree-of-freedom system. The dynamic response in one period is obtained based on the forced vibration theory of multiple-degree-of-freedom system. The analysis shows that the value of natural frequency of longitudinal vibration of constrained trajectory conveyor chains with long pitch is large and the vibration response in no-load operating condition is weak. In another word,the vibration is improved greatly with the constrained trajectory.