The paper deals with the bending of a composite beam-column of variable cross-section. The governing equation is developed under usual assumptions concerning the beam-column deformation (the deformation is not small enough to neglect its effect on the equilibrium equations, but it is sufficiently small for geometrical linearization to be carried out) and it refers to any given creep function. A simply supported beam-column of constant cross-section under particular external load is considered as example to show the application of the developed equation and the solution method. Introducing a particular creep function and geometrical properties of cross-section into the general result the known interval in which the values of Euler's critical force lie is obtained as well as the safe load limit.