Most living tissues are composite materials with highly nonuniform material properties. Their structure and composition vary from point to point. There are also changes in strength and stiffness, with age and disease condition, which affect the biological function of the tissue. Therefore, the knowledge of tissue mechanical properties on the nano/micro scales is critically important. We have developed an approach to extract the elastic moduli of highly inhomogeneous biological tissues with surface defects that cannot be well characterized. The robustness of our method is illustrated on the example of cartilage extracellular matrix. The tissue was mildly crosslinked to prevent proteoglycan loss due to diffusion occurring upon tissue slicing. Thin tissue slices (~12 μm) have a poorly defined surface layer due to the damage and stress release caused by sectioning. Under indentation forces, the tissue exhibits apparent strain-stiffening, an artifact of the presence of this layer. Therefore, this layer must be accounted for if the properties of the intact, bulk matrix are to be correctly probed. To separate out the effect of this damaged layer, we used large indentations with the mechanics model for finite sample thickness and included an additional constant force contribution from the surface layer as well as the contact point of the underlying intact layer as fitting parameters. This in effect is equivalent to allowing for the existence of an effective\contact point that is computed as a best-fit parameter. By not forcing the fitted contact point to be on the force curve and by applying larger indentations, we obtain the elasticity of an equivalent material undergoing similar indentation but having a smooth, undamaged surface. Such an approach not only gave us an elasticity modulus that remained unchanged with indentation depth, but also had good correlation across length scales. This explains previous observations that the Hertz model cannot satisfactorily probe matrix mechanics and instead, large deformation models need to be employed (Lin et.al, Biomech. Model. Mechanobiol., 2009). Comparing the contributions from the intact matrix alone, we found that the cartilage stiffness increases towards the resting zone but decreases in the proliferative zone, even though the chemical composition does not change significantly between these regions.