A computer program for the linear and nonlinear analysis of shell structures (STAGS) is applied to the instability analysis of a complex stiffened structure subjected to complicated sets of distributed and concentrated loads. Results obtained from two-dimensional bifurcation and nonlinear collapse analyses are presented. The nonlinear analysis includes the effects of an imperfection in a shell stiffened by heavy longerons. Several problems associated with the analysis of very large eigenvalue problems are discussed (one case involved a model with 20,910 degrees-of-freedom). These include the use of the appropriate finite-difference formulation to ensure convergence in a desired direction (approaching the asymptotic value either from above or from below) and the use of variable grid spacing to induce buckling in one part of the structure or the other. A technique of finding higher eigenvalues by removing the prestress at the point of bifurcation is described.