Abstract The aim of this study was to relate observed low-cycle fatigue response under asymmetric loading to mean stress effects on the cyclic behaviour and fatigue life of nickel-base Incoloy 901 superalloy at room temperature. Based on experimental data, a mean stress relaxation model was proposed, which described the dependence of mean stress on the total strain range and on cyclic plasticity. It was found that cyclic softening and mean stress relaxation began when plastic strain started to develop, and increased in importance with increasing strain range. Both depended on the plastic strain range rather than on monotonic plastic deformation. For any given strain ratio there was a value of strain range corresponding to peak mean stress sustained. Beyond this strain range, mean stress relaxation began. A mean stress strength constant representing the apex on the σ m axis of the Goodman diagram was introduced in order to modify the Goodman criterion, resulting in a modified strain-life relation. Both the mean stress-relaxation model and the strain-life model were evaluated against LCF test data.