The China Initiative Accelerator Driven System (CiADS) was proposed by China Academy of Science since 2015. The subcritical reactor in CiADS is a liquid Lead Bismuth Eutectic (LBE) cooled fast reactor. When the reactor core is in operation, the LBE coolant will directly contact and corrode the inner surface of reactor vessel. Due to the high temperature, the corrosion will be more severe. If the stress on the reactor vessel exceeds the limit, the plastic deformation will occur, leading to the generation and expansion of defects and cracks, and the safety of the reactor will be affected. Therefore, evaluating the stress field of the reactor vessel under different operating conditions is a very important research project. In this paper, the finite element analysis software ADINA was applied to analyze the reactor vessel in CiADS, and the ASME Code was used as stress assessment standards. We can preliminarily prove that the stress assessments of the vessel during the postulated Unprotected Loss of Flow (ULOF) accidents satisfy the requirements of ASME Code. The limit reactivity insertion to protect the vessel from plastic deformation is 0.58$ in the postulated Unprotected Transient over Power (UTOP) accidents based on our current results. Therefore, we can preliminarily conclude that the current material selection and structural design of the reactor vessel in CiADS could survive most of the postulated transient accidents considering the stress effect.