Ion effects are potentially detrimental to the performance of the damping rings for the International Linear Collider (ILC). In this paper, the ion effects in ILC damping rings are briefly reviewed. The fast beam-ion instability (FBII) is studied in the linear regime. The growth time and the tune shifts at bunch train end due to FBII are analytically calculated and compared for two variants of the ILC damping ring designs (OCS and TESLA) and discussed as a function of the vacuum pressure. Finally, some simulation results are also given.