This theoretical investigation is concerned with stress distribution in the vicinity of the vertex of an orthotropic elastic orthogonal wedge subjected to admissible boundary conditions. By admissible boundary conditions it is meant that the normal and tangential boundary conditions N(s) and T(s), respectively, are such that ∝0∞¦N(s)¦2 d s and ∝0∞¦T(s)¦2 d s are finite. The axes of the orthotropy of the wedge are assumed to coincide with axes of the coordinate system. In this analysis, Fourier-Plancherel integral transform is used to solve the boundary value problems of orthotropic elastic half plane and to solve a system of integral equations for which the kernels ki (t,s), i = 1,2, do not satisfy the necessary Fredholm's. alternative ∫0∞∫0∞|ki(t,s)|2dt/ds < ∞, i = 1,2. The problem of elastic orthotropic orthogonal wedge is divided into four basic problems each of which is characterized by relevant generalized Green's functions. These generalized Green's functions are evaluated analytically as well as numerically. Knowing these generalized Green's functions, special formula is developed to calculate the stresses at any given point in the wedge for any arbitrary admissible boundary conditions.A special form of Filon's method is used to evaluate improper integrals with rapidly oscillating integrands. The whole procedure of calculating stresses is illustrated by an example.