The behavior of a circular rigid beam on a two-parameter elastic foundation which can not support tension stresses is analyzed. The vertical displacement field of the foundation is expressed in series form which satisfies the related governing differential equation. Later, for evaluation of the unknown constants, this displacement field is combined with that of the circular rigid beam which consists of a rigid translation and a rigid rotation by considering conditions related to contact and lift-off regions. It is shown that the problem displays a highly non-linear character due to the lift-off of the beam from the foundation and the numerical treatment of the governing equations can be accomplished by adopting iterative processes in terms of the applied force and moment as well as the contact angle. Numerical examples are reported for various cases to verify the present formulation and to demonstrate the non-linear behavior of the beam. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.