"Shells under compressive loading investigated under the assumption of perfect properties may be considered to be optimal structures. Their load carrying capacity is significantly larger compared to shells which show deviations in geometry, material behaviour, loading and boundary conditions. ...Unfortunately, comparatively little quantitative information exists about the initial imperfections in actual structures... One possibility to improve this situation is to perform systematic numerical simulations... Classical numerical concepts of the load carrying capacity of imperfect structures focus on the model of a perfect shell configuration and on the analytical estimation of unstable, postcritical equilibrium paths. This was first demonstrated by Koiter, whose postbuckling theory describes the nonlinear static load carrying behaviour of structures in the initial stages of buckling. ...[I]nitial unfavourable imperfections will lead to a reduction in load carrying capacity. This approach has certain restrictions as the results are evaluated by linearisation around the bifurcation point of the perfect shell. For the numerical simulation of the load carrying behaviour of imperfect shells it is commonly assumed that the initial geometric imperfections have the shape of the lowest bifurcation mode of the respective shell. ...In the cases of high imperfection sensitive shells [with] multi-mode-buckling... the lowest bifurcation mode is not always the ”worst” imperfection shape. Recently, a specific concept employing finite element procedures... directly evaluates the ”worst” imperfection shape and [is based upon] analysis of the imperfect shell space."