The classic strength of materials theory considers out-of-plane stresses in beams subjected to pure bending to be negligible. This work undertakes a theoretical analysis of this proposition by basing it on the development of the Airy's functions in polar coordinates. The purpose of this research is studying the effect of this kind of stresses in structures fabricated with non-isotropic materials. Specifically, multi-component sandwich beams subjected to pure bending and large deflections have been studied. An analytical model is proposed that allows these out-of-plane stresses to be calculated according to the curvature change and other design parameters of the specific structure. The completed model was used to calculate the out-of-plane stresses for different design configurations, in order to study their effects. Finally, results are compared to a finite element model.