Abstract: In the problems of inserting the catheter and steel pipe into the wellbore, the buckling problem of variable-length slender rods is often involved. The buckling governing equation of variable-length slender rods is established based on the principle of minimum potential energy and the Lagrange multipliers method. The buckling response of variable-length slender rods under clamped boundary conditions is derived from the elliptic integral method. The numerical calculations are performed to illustrate that due to the change in length, configuration force is generated after the structural buckling, and the configuration force significantly affects the buckling response.