Based on the non-linear differential equations of buckled pipes, the buckling behavior of pipes in different wellbores has been analyzed. The relation between the deflection of buckled pipe and the loads on it has been given, and the critical loads for sinusoidal and helical buckling within different wellbores subjected to axial and torsional loads have been determined. Therefore, the profile of load increase during the post-buckling process and the bending moments in the buckled pipe can be determined. In addition, the effects of down-hole packer as fixed end on the helical buckling behavior of pipes have been investigated. These results can be applied to the related engineering design and construction.