The present work is a study of the stress and displacements field in 3D corners. The corner represents the stress concentration along edges or in its vertex; each one has different asymptotic solutions. In this work, the solution in the vicinity of edges concentrates our attention. The elastic solutions can be decomposed as the sum of 2D elastic field called fundamental singular field and the second higher-order field called shadow field. The properties of eigen-functions, eigen-values and Edge Stress Intensity Functions (ESIFassociated with both fields are analyzed. It develops a general method for calculating the eigen-values and eigen-functions. The shadow functions depend on the fundamental singular function and its deduction established clearly through equations governing of the problem. A new method based on conservation integral is introduced for determining the ESIF, which leads to a new domain-independent integral defined along the edge. A proof of the domain integral independency, based on the bi-orthogonality of the two-dimensional eigen-solutions associated to a corner problem, is presented. The new numerical approach is developed for extraction the ESIFs from a solution obtained by the Boundary Element Method (BEMwhich are relevant for a failure assessment of mechanical components.