The classical formula for the buckling load of axially compressed cylindrical shells predicts 4-5 times higher critical load than observed in experiment. The discrepancy is explained by high sensitivity of the buckling load to imperfections. However, the exact mechanism of this sensitivity remains elusive. Our rigorous theory of "near-flip" buckling of slender bodies reveals a scaling instability of the critical load caused by imperfections of load. A possible mechanism of sensitivity to imperfections of shape can also be seen in our analysis. This is a joint work with Davit Harutyunyan.