Cracking behavior in low cycle fatigue regime depends on the level and the multiaxiality of the applied stress and also on the microstructure. Such a complex cracking behavior affects failure life significantly. More realistic assessments of failure life and integrity require a new appropriate procedure to analyze the crack growth process in multiaxial fatigue. A model of the fatigue process has been proposed to describe the cracking behavior in biaxial stress state. There is, however, no adequate model to present features of material microstructure. In this work, simulations of crack initiation and propagation based on a previous model were carried out in microstructure modeled by using Voronoi-polygon. In a crack initiation analysis, slip-band crack was modeled for the slip system given randomly in each grain composing the modeled microstructure. In modeling crack growth, a competition model between the coalescence growth and the propagation as a single crack was applied. Simulated cracking morphology and failure life were compared with experimental results observed in biaxial fatigue using circumferentially notched specimens of a pure copper, and the applicability of the proposed model was discussed.