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• Theoretical solution of an elastic-plastic crack in a half plane is presented. • Theoretical modeling of crack-tip plasticity in a strain-hardening material. • Theoretical modeling of plasticity at the mixed-mode crack tip. • Crack plane displacement is predicted accurately by the theoretical modeling. The crack growth behavior is influenced greatly by the crack-tip plasticity. Most of the existing two-dimensional (2D) theoretical models of crack-tip plasticity are appropriate only for elastic perfectly-plastic materials under simple mode load, which limits the application range. This paper presents a theoretical model based on the distributed dislocation technique (DDT) that can be used at mixed loads with bilinear strain-hardening and perfectly-plastic materials. The problem of a half plane containing an edge crack under uniaxial tensile load or mixed loads is considered in both 2D limit cases: plane stress and plane strain. The theoretical modeling results are compared with finite element simulations. The results show the developed models are suitable for strain-hardening materials under mixed loads, which is a new progress in the theoretical modeling of crack-tip plasticity. [ABSTRACT FROM AUTHOR]