Strain-based engineering critical assessment methods allows certain amount of plastic strain during installation and in service, for pipelines crossing seismically-active areas. Most strain-based engineering critical assessment methods are established for materials with smooth stress-strain relationship, leaving the so-called Lüders plateau influence on ductile fracture response seldomly explored. This work studied the effect of the Lüders plateau on mode I ductile crack growth with the modified boundary layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model was implemented and the Gurson damage model was selected to simulate crack propagation. Factors including the plateau length and softening modulus in the “up-down-up” constitutive model, strain hardening of the matrix material and the initial void volume fraction parameter were analyzed. Numerical results show that the Lüders plateau modifies the crack tip constraint and the damage evolution, and the plateau length plays the dominant role on ductile crack growth behaviour in the presence of Lüders plateau.