The initial postbuckling behavior of axially stiffened cylindrical shells is studied with a view to ascertaining the extent to which various effects such as stringer eccentricity, load eccentricity, and barreling influence the imperfection-sensitivity of these structures to buckling. In most cases, when these effects result in an increase in the buckling load of the perfect structure, they increase its imperfection-sensitivity as well. In some instances, however, barreling can significantly raise the buckling load of the shell while reducing its imperfection-sensitivity. The analysis, which is based on Koiter’s general theory of postbuckling behavior and is made within the context of Ka´rma´n-Donnell-type theory, takes into account nonlinear prebuckling deformations and different boundary conditions.