Stress relaxation and inelastic strains accumulated in ligaments of perforated plates subjected to cyclic plastic straining followed by creep relaxation are analyzed. Due to elastic follow-up the stresses, especially in thin ligaments, do not relax as fast as predicted by the uniaxial model for zero total strain rates.A simple strip model of the ligament is developed to account for its non-uniform width. Elastic follow-up factors based on this model are determined and used to bound the relaxation stresses at the hole boundaries for creep rupture damage evaluation. Plastic strain concentrations obtained for monotonic loading are used to bound strain ranges at hole boundaries needed for fatigue evaluations.