We provide analytical solutions for the full stress field of straight sandwich beams with identical skins subject to linear elastic flexure governed by zigzag warping, where all layers obey Timoshenko's kinematics. As a main novelty, we make use of a balance equation for the Cauchy continuum to recover of the through-the-thickness normal stress component, σy. The new estimates are accurate for a wide range of relative stiffness between skins and core and suitable boundary conditions, as it can be demonstrated through the comparison with detailed finite element simulations where the sandwich is modelled as a two-dimensional continuum. As a main practical result concerned with the study of delamination, we find that at a core-skin interface of a cantilever sandwich subjected to a uniformly distributed load, in a region close to the fully-clamped crosssection, σy is a tensile stress of magnitude larger than that of the shear stress. On this basis, we infer that the availability of good estimates for σy , along with those for the longitudinal and shear stresses, may be important for the accurate design of sandwich