Many structures are hierarchical in nature and are made up of substructures distributed across several length scales. Examples include aircraft wings made from fiber reinforced laminates and naturally occurring structures like bone. From the perspective of failure initiation it is crucial to quantify the load transfer between length scales. The presence of geometrically induced stress or strain singularities at either the structural or substructural scale can have influence across length scales and initiate nonlinear phenomena that result in overall structural failure. In this presentation we examine load transfer between length scales for hierarchical structures when the substructure is known exactly or only in a statistical sense. New mathematical objects beyond the well known effective elastic tensor are presented that facilitate a quantitative description of the load transfer in hierarchical structures. These quantities are introduced within the mathematical frame work of G-convergence for elliptic operators. Several concrete physical examples are provided illustrating how these quantities can be used to quantify the stress and strain distribution inside multi-scale structures.