This work aims at evaluating the elastic modulus of hard biological tissues by considering their staggered platelet micro-structure. An analytical expression for the effective modulus along the stagger direction is formulated using three non-dimensional structural variables. Structures with a single staggered hierarchy (e.g. collagen fibril) are first studied and predictions are compared with the experimental results and finite element simulations from the literature. A more complicated configuration, such as an array of fibrils, is analyzed next. Finally, a mechanical model is proposed for tooth dentin, in which variations in the multi-scale structural hierarchy are shown to significantly affect the macroscopic mechanical properties.