In many practical problems of plate and shell buckling, the pre-buckling state is linear and can be obtained from the linearized equations of elasticity. The computation of the buckling load and mode in such cases correponds to a linear eigenvalue problem that can easily be formulated and implemented in a finite element code. This report describes a procedure for buckling analysis that is based on these simplified initial conditions. The algorithm is useful as a tool for preliminary studies. It can also be used as a basis for post-buckling analysis with continuation methods.