Mandel established the principle of correspondence, by means of which equations for linear viscoelastic materials with aging are obtained from equations of linear elasticity. The paper provides an extension of Mandel's principle to the case of a linear support in which a homogeneous linear visco-elastic material with aging is coupled with one or more elastic materials. The application of linear integral operators allows to derive expressions for stresses and displacements in coupled linear supports, while linear viscoelastic material with aging is introduced for concrete. For the observed transverse average, a system of two inhomogeneous integral equations is established as a connection between cross-sectional forces and deformation quantities. From this system of equations and its solution, a correspondence is established with the corresponding equations for the support that is made of homogeneous elastic material, so that the geometric characteristics of the corresponding section are formally replaced by operators. The functions associated with the other operators are unique solutions of two independent integral equations of Voltaire type II. By using the principle of correspondence, expressions for stresses and displacements for a coupled support are obtained directly from the expressions known in the Resistance of Materials, which are valid for a support made of homogeneous elastic material.