The study and design of the vacuum system requirements of free electron laser had been accomplished. The total required time for evacuation has been studied by comparing it with the final required pressure. Some parameters of the vacuum chamber such as the length of the vacuum chamber and the total time of evacuation have been compared with the final required pressure to complete the design of the system with all calculation needed for the design. Also the leaks have been predicted through the vacuum operation. A cylindrical vessel for a sample that has been suggested for Free Electron Laser has been designed with small dimensions.According to this study all the data that devote with the vacuum system have been calculated and the engineering and clarification drawings of the system have been studied. And it insures that the leaks of this sample are very little so it negligible. The effect of the residual gas inside the vacuum chamber has been studied and insures that this effect did not change the direction of the electron beam, the charge of the electron, and the velocity of this electron by comparing the ratio of energy loss ofelectron with the final required pressure.