In this study, circular beams with variable cross-sections on elastic foundations under arbitrary loading are analyzed by the finite element method. The Winkler hypothesis is considered for the foundation. With the developed circular finite element CR12, in which six independent variables are chosen for each node, all kinds of boundary conditions can be taken into account. In this study the effects of shear deformation and torsional effect of the foundation are included. Additionally, a special case finite element formulation is given for straight bars on elastic foundations. Copyright (C) 1996 Elsevier Science Ltd.