Application of Koiter's general buckling and post-buckling theory by using a generalized strain-displacement relationship which in fact represents a slightly non-linear stress-strain constitutive relationship is investigated. It seems that a slight non-linearity in the stress-strain curve may lead in some cases to unexpected large reduction of the classical buckling load. The non-linear constitutive law is not consistent with the basic assumptions of Koiter's theory. It is shown that a strain-displacement relationship obtained by the use of Taylor's series is preferable. For complicated structures calculation errors are inavoidable. A straight forward application of Koiter's theory for such structures would lead to incorrect interpretation. A method to avoid such a difficulty is proposed and both analytically and numerically described.