In this work, the crack initiation and propagation process in the microstructure of the cortical bone is simulated using the finite element method combined with a mesh fragmentation technique. Thus, triangular finite elements with high aspect ratio (elements with the base much greater than the height) are inserted in pairs between the interfaces of regular triangular elements, after the fragmentation process to describe the possible crack path trajectories. The microstructure of the cortical bone is modeled as a 4-phased composite material: interstitial matrix, cement line, osteon and Haversian canal. The material non-linearity is represented by the behavior of the high aspect ratio elements via a combined damage model with adequate mechanical properties assigned to each phase of the material. The methodology is employed in the numerical simulations of 6 conceptual representations of the microarchitecture of the cortical bone and 1 model based on the geometry extracted from a digital picture. The mechanical behavior is assessed in tension and bending tests while considering geometries with one or multiple osteons. The results demonstrated that the proposed technique based on the mesh fragmentation process is suitable to represent the crack initiation and propagation process in the cortical bone, with results in good agreement with those available in the literature, including the mechanical influence of the cement line in the cracking process.