In this chapter, we treat initial geometric imperfections as spacewise random functions (i.e., random fields). As a result, the buckling load the maximum load the structure can sustain turns out to be a random. We focus our attention on reliability of the shells, namely the probability that a structure will not fail prior to the specified load. We develop efficient techniques of simulation of random fields, based on the knowledge of the mean initial imperfection function and the auto-correlation function. This allows us to conduct, by the Monte Carlo method, an extensive analysis of the buckling of columns on non-linear elastic foundations and of circular cylindrical shells. We consider the cases of both axisymmetric and general, non-symmetric imperfections.