The purpose of this paper is to describe the initial postbuckling behavior of cylindrical shells under axial compression. Our thesis is that, out of a single infinity of possible buckling configurations which all correspond to diamond-shaped patterns, the square diamond pattern dominates. We do not claim that this pattern will be seen under all circumstances; we do claim, however, that if no substantial bias is present in either the initial imperfections or initial conditions, a natural selection mechanism exists which favors the square diamond configuration. In this paper we carry out the analytic work. A multiple scale technique is used to describe both the dynamic interaction and evolution of competing diamond patterns and the propagation of spatial inhomogeneities. Stability analysis on the resulting differential equation system lends support to our stated thesis. In addition, some initial numerical studies are presented which verify our conclusions. Part 2 will be devoted to more extensive numerical experiments.