An exact solution for the stress field within a rectangular slab of orthotropic material is found using a two-dimensional Fourier series formulation. The material is required to be in plane stress, with general stress boundary conditions, and the principle axes of the material must be parallel to the sides of the rectangle. Two load cases similar to those encountered in materials testing are investigated using the solution. The solution method developed is seen to have potential uses in stress analysis of composite structures. / Master of Science