In the present paper the stiffness matrix of the fixed-end composite member, which is usually called a member type of "k" is derived. The elements of the stiffness matrix are determined without mathematical negligences. The solutions contains only the inevitable approximation concerning the desrip-tions of the rheological properties of materials. Concrete is considered as an aging linear viscoelastic material. The relaxation of the prestressing steel is taken into account . The expressions arc developed for any given concrete creep function and for a member of variable cross section. Following these expressions, as a special case, the expressions for the member of constant cross section are derived. Using this kind of operators the problem is solved not only symbolically and formally but also the expressions for stresses and displacements are significantly simplified.