Aim of the present study is to analytically show that the cross-sectional taper in non-prismatic slender solids produces stress fields that are absent in prismatic ones and are unpredictable by resorting to the results valid for these latter, as it is done in stepped beams. To this end, the equations that govern the state of stress and strain in tapered slender solids susceptible to large deflections are obtained via a variational approach, in the form of partial differential equations and related boundary conditions. Such equations admit closed-form solutions in few cases, e.g., for circular cross-sectioned tapered beams subjected to forces and moments applied only at the end cross-sections. By considering this paradigmatic case, an analytical demonstration is here provided about the inadequacy of stepped-beam approaches when dealing with stress predictions in tapered structural elements.