An analytical model describing the elastic response of a system of coaxial thick-walled cylinders in contact is presented. The materials from which the cylinders are constructed must exhibit orthotropic elasticity. The loading can be uniaxial tension, torsion or internal pressure. The model allows inter-and intralaminar stresses to be determined. Examples of applications include pipes and light weight drive shafts reinforced with a helical winding, composite pressure vessels and single cells from fibrous plants such as flax and hemp.