To perform a safety assessment for the geological disposal of radioactive waste, it is important to understand the response characteristics of the disposal system. In this study, approximate analytical solutions for steady-state nuclide releases from the engineered barrier system (EBS) of a repository were derived for an orthogonal one-dimensional diffusion model. In these approximate analytical solutions, inventory depletion, decay during migration and the influence of groundwater flow in the excavation damaged zone (EDZ) were considered. These solutions were simplified by the Taylor theorem in order to clearly represent the response characteristics of the EBS. The validity of these solutions was shown by comparison with numerical solutions. The response characteristics of the EBS are useful for identifying target values for important parameters that would have the effect of improving the robustness of system safety. The robustness of the geological disposal system and the reliability of the safety assessment can thus potentially be improved using the approximate analytical solutions.