Summary The need to improve completion reliability has prompted a second, deeper look at the analysis of tubing buckling. The conventional-buckling analysis is assumed to hold "far from the packer", but what happens "near" the packer? The original development by Lubinski and Woods used the method of virtual work to determine a constant pitch helix. All attempts to connect a constant pitch helix to boundary conditions, such as a packer, have failed. The conventional wisdom says that the virtual work solution applies "far from the packer". How far is this, and what happens between the packer and this point? Even worse is the case of tapered strings. The generally accepted answer to the tapered string problem is a "stacked" set of Lubinski solutions, with each solution far from the interconnection of the different sized tubulars (1962). Perhaps there are nonconstant pitch solutions? Because the buckling-differential Eq. is nonlinear, it is not surprising that no other analytic solutions have been discovered until recently. Once these solutions are known, the initial value problem can be posed and solved. Two possible boundary conditions are considered in this study: a cantilever boundary condition to model a packer, and a "pinned" boundary condition to model a centralizer. For the first time, analytic solutions were found for both problems, and interestingly, both solutions converged rapidly to Lubinski's constant pitch solution at a specified distance from the boundary. For this reason, many of the original Lubinski calculations remain essentially correct, (such as length change and contact forces). Alternatively, the bending moment near the boundary exceeds the bending moment calculated from the Lubinski solution by approximately 20%. For this reason, conventional pipe-buckling stress analysis must be revised. Further applications of these solutions allow different sized tubulars to be interconnected, solving the tapered-string problem for the first time. An additional, useful result is the solution to the helix "reversal" problem. The principal applications for these solutions are the stress analysis and design of tubing and casing strings. The boundary solutions are simple formulas, suitable for spreadsheet or hand calculations.