Abstract: The buckling behavior of the rod string in a wellbore is one of the key issues in petroleum engineering. The slender rod string in a wellbore is studied in this paper. According to the sinusoidal and helical buckling geometries of the pressurized column, the post-buckling contact friction state between the rod string and the wellbore is considered. The Lagrange multiplier method is used to describe the sliding displacement boundary conditions for the wellbore and the gravitational potential energy and the friction dissipated energy are used in the energy method. The contact force and the friction resistance between the rod string and the wellbore are derived for vertical wells. The post buckling experimental apparatus is developed in this paper. The sinusoidal and helical buckling critical loads and the friction resistances are derived under different loads. The experimental results agree with the theoretical results. This paper provides an effective method for buckling columns, such as drilling, coiled tubing.