Most analytical calculation techniques of the stress state in multi-structural elements (MSEs) are based on the assumption that the layers are deformed only in the direction of the load applied. Consequently, deformations in the perpendicular directions do not appear, or in case they do, the deformations are equal, and therefore, have no impact on the stress state. It is well-known that materials do not only exhibit deformations in the direction of the force applied, but in perpendicular directions as well. MSEs are made of materials with different mechanical properties; therefore the deformations of the layers in transverse directions also differ. As a result, strains emerge in those directions. Consequently, the layers of MSEs are subjected to a complex, multi-axial stress state. The subject of the present work is MSEs with a rectangular and circular/annular cross section, subjected to the axial load, internal pressure and change of the temperature. Materials of the layers are isotropic, homogeneous and linearly elastic. The MSEs considered are made of layers with the thickness much smaller than their width/length.