  We revisit the classical problem of the buckling of a long thin axially
compressed cylindrical shell. By examining the energy landscape of the perfect
cylinder we deduce an estimate of the sensitivity of the shell to
imperfections. Key to obtaining this is the existence of a mountain pass point
for the system. We prove the existence on bounded domains of such solutions for
all most all loads and then numerically compute example mountain pass
solutions. Numerically the mountain pass solution with lowest energy has the
form of a single dimple. We interpret these results and validate the lower
bound against some experimental results available in the literature.
