In this article a superposition method for analysing an orthotropic elastic rectangular with arbitrary boundary conditions is presented. Two solutions in trigonometric series derived by the method of initial functions are used to construct a general solution for a rectangle in 2-dimensional Cartesian coordinates. Boundary conditions lead to a system of linear algebraic equations over the unknown coefficieints of the series expansion of the general solution. The approach is used to analyse a clamped isotropic and orthotropic console rectangle.