Abstract: To ensure the consistency of the minimum of energy functional with its corresponding equilibrium equation eigenvalue, differential quadrature (DQ) element is established based on the equilibrium equation and natural boundary conditions of a column subjected to radial constraint. Sinusoidal buckling loads of a column segment constrained in a circular tube are analyzed under nine different end constraints. A comparison with the theoretical solution and the experimental data demonstrates the rationality of the proposed model and method. The sinusoidal buckling load of a segment of drillstring constrained in an inclined wellbore is analyzed by using the DQ element method. The effects of oblique angles of wellbores and end constraints on the buckling loads are investigated. The numerical results are compared with those of finite element method, demonstrating that the DQ element method has advantages of higher accuracy and strong reliability. Some references for engineering practice are given.