The diffusion of tritiated water vapor into concrete walls of a fusion reactor building is studied to evaluate the capability of the tritium containment of concrete materials. First, depth profiles of tritiated water in concrete are calculated to evaluate the capacity of the tritium containment by the sound concrete without cracks, and a 0.5-m-thick concrete wall is sufficient to prevent tritiated water releases to the environment in a normal operation of a fusion reactor over 50 yr. Second, simulations of the cleanup of tritiated water in the concrete reactor hall atmosphere taking into account the soaking are performed. Concrete porosity should be decreased to shorten the cleanup time of the reactor hall atmosphere. Surface coatings on the concrete, which apparently decrease the surface porosity, are effective measures to prevent the diffusion of tritiated water vapor into concrete during accidental releases.