Abstract: In order to investigate the effect of the microstructure of intermetallic compound (IMC) on the micro and macro mechanical behaviors of solder joints, a finite element based numerical approach is developed to simulate initiation, propagation and coalescence of microcracks along the grain boundaries in the IMC layer. In the approach, the topological microstructure of IMC grains is generated by Voronoi tessellations, and the proposed cohesive interface elements are embedded between the grain boundaries. By the proposed approach, the effect of grain shape and randomly distributed grain interfacial defects on the microcrack pattern and the overall response, and the effect of IMC microstructure on the strength and the failure mode of solder joints, are investigated. The results indicate that the grain shape has little effect on the overall mechanical response, but affects the cracking path. In the model with Weibull distributed grain interfacial strength, the weak grain interface plays a key role in the overall strength. The thickness of the IMC layer has a significant influence on the strength and failure mode of solder joints, while the roughness of the solder/IMC interface has an influence on the failure mode only.