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In order to take into account the local material non-linear elastic-plastic effects generated by notches, Glinka proposed the equivalent strain energy density (ESED) Criterion which has been widely accepted and used in fatigue theory and calculation for the last few decades. In this paper, Glinka's criterion is applied to structural optimization design for elastic-plastic correction to consider material non-linear elastic-plastic effects. The equivalent (fictitious) stress was derived from Glinka's Criterion equation for the commonly used Ramberg-Osgood and bi-linear stress and strain relationships. This equivalent stress can be used as the stress boundary constraint threshold in structural optimization design to control the elastic-plastic stress or strain in nonlinear optimization.