Buckling of stiffened plates with arbitrarily oriented stiffeners and of shells are considered. The main objective of the work, presented as a thesis for a cand. scient. degree (master equivalent) at the University of Oslo, has been to develop computational models for direct calculation of the structural response using the Rayleigh-Ritz method. The deflections are represented by trigonometric functions. All combinations of biaxial in-plane compression, tension and shear are included in the formulations. Estimation of the ultimate strength is found using the first yield as the collapse criterion. The formulations derived are implemented in a Fortran computer code. Numerical results are obtained for a variety of stiffener orientations and geometries. The results are compared to finite element analysis results and are found, in most cases, to be conservative compared to the finite element calculation results.