Glaucoma is among the leading causes of blindness worldwide. The disease involves damage to the retinal ganglion cell axons that transmit visual information from the eye to the brain. Experimental evidence indicates that biomechanical mechanisms at different length scales are involved in pathophysiology of glaucoma, where chronic intraocular pressure (IOP) elevation at the organ level initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa consists of a porous collagen structure through which the axons of retinal ganglion cells (RGCs) pass on their path from the retina to the brain. The extent to which the structural mechanics of the lamina cribrosa contribute to the axonal insult remains unclear. In this book chapter, we give a short review of the present understanding of the structural mechanics of the lamina cribrosa and its role in glaucoma. The main aim is to present a first computationally coupled two-scale analysis of the lamina cribrosa that translates the IOP load at the macroscale to the mechanical insult of the axons within the mesostructure of the lamina cribrosa. The numerical results of two-scale analysis suggest that the collagen structures of the lamina cribrosa and its surrounding peripapillary sclera effectively provide mechanical support to the axons by protecting them from high tensile stresses even at elevated IOP levels. However, in-plane shear stresses in the axonal tissue may increase with increasing IOP at the posterior lamina insertion region and contribute to a mechanical insult of the RGC axons in glaucoma.