A study of elastic stability is presented for annular plates with uniform and non-uniform thickness with the outer border subjected to hydrostatic pressure under differing border conditions. An approximate solution is proposed using polynomial coordinate functions which identically satisfy the boundary conditions only at the outer edge. The eigenvalues were determined using the Rayleigh-Fritz Optimized Method and were compared with results obtained using the Finite Elements Method. These results allowed to know the critical load in integral structural elements of containers or tanks submitted to external pressures. An application in rigidified cistern tanks submitted to external pressure and to vacuum, is presented. The results permitted the conclusion that the methodology employed was satisfactory and applicable to other types of materials.