A computational multiscale model of damage mechanisms and strength of lamellar bone is presented. The analysis incorporates the hierarchical structure of bone spanning the nanoscale (mineralized collagen fibril), the sub-microscale (single lamella) and the microscale (lamellar structure) levels. Due to the presence of several constituents (collagen, hydroxyapatite minerals, and non-collagenous proteins) and the different microstructural features at each scale, various deformation and failure mechanisms occur in bone at its several levels of hierarchy. The model takes into account the dominant damage mechanisms at the above mentioned three scales and predicts the strength of bone by using a cohesive finite element method. Elastic moduli of bone at these three different scales are also obtained as part of these calculations. The obtained modeling results compare well with other theoretical and experimental data available in the literature.