Steady-state problems of stresses in orthotropic slabs subjected to forces and temperature distribution on the faces are solved by means of Fourier transforms. The usual direct applications in the literature are shown for simple examples to lead to divergent integrals but, by introduction of generalized transforms, a very broad class of problems can be handled. As a part of these considerations, a more definite form of Saint-Venant’s principle is obtained. For a certain class of material constants, it is possible to obtain closed-form solutions for stresses when concentrated loads or temperature sources are applied to the faces of the slab. Results are presented for several examples in the form of complex stress potentials and graphs of the corresponding stress components.