With the development of drilling technology,the oil/gas well has evolved from its early vertical straight form to the inclined,horizontal,plane curved,or even 3D curved well-bore.Understanding of the buckling behavior of a drill-string in a well-bore is crucial for the success of a drilling operation.Therefore,equilibrium equations for analyzing the buckling behavior of a drill-string in a 3D curved well-bore are required.Based on Love’s equilibrium equations for a curved and twisted rod in space,a set of equilibrium equations for the nonlinear buckling analysis of a drill-string in a 3D curved well-bore are derived by introducing a radial constraint of the well-bore.The proposed formulae can account for the well curvature and tortuosity.Thus,it can be used to analyze the buckling behaviors of a drill-string constrained in a well-bore and subjected to axial compression,torsion at its upper end,and gravity simultaneously.It is worth noting that the existing equations in the literature for a drill-string in a straight and plane curved well-bore with a constant curvature are a special case of the proposed model.Thus,the present model can provide a theoretical basis for the nonlinear buckling analysis of a drill-string constrained in a 3D curved well-bore. With the development of drilling technology, the oil / gas well has evolved from its early vertical straight form to the inclined, horizontal, plane curved, or even 3D curved well-bore. Understanding the buckling behavior of a drill-string in a well -bore is crucial for the success of a drilling operation. Before, equilibrium equations for analyzing the buckling behavior of a drill-string in a 3D curved well-bore are required. Based on Love’s equilibrium equations for a curved and twisted rod in space, a set of equilibrium equations for the nonlinear buckling analysis of a drill-string in a 3D curved well-bore are derived by introducing a radial constraint of the well-bore. The proposed formula can be for the well curvature and tortuosity.Thus, it can be used to analyze the buckling behaviors of a drill-string constrained in a well-bore and subjected to axial compression, torsion at its upper end, and gravity simultaneously. It is worth noting that the existing equations in the literature f or a drill-string in a straight and plane curved well-bore with a constant curvature are a special case of the proposed model.Thus, the present model can provide a theoretical basis for the nonlinear buckling analysis of a drill-string constrained in a 3D curved well-bore.