The most ship structures are composed of plate elements. When appropriate stiffeners are furnished on plates, the buckling strength of the plates increase effectively, as well as their bending rigidities. The finite element method has been expanded to analyse the buckling strength of ship structures. While the finite element method is very useful, the size of equations obtained by the method is extremely large. In the paper, a powerful eigenvalue economizer technique was introduced, which reduces the degrees of stability problems. As a basic example of the application, the accuracy of the solution by the technique using the finite element method was examined for several kinds of stiffened plates in relation to the number of degrees of freedom. The authors discussed mathematical meaning of the eigenvalue economizer technique. Variable informations are obtained on variables which are eliminated from the characteristic equation. Finally, the buckling strength of transverse ring of large tanker was analysed, varying the location of stiffeners. It was found that the ship structure without any stiffener buckles under applied load. While, the structure with horizontal and diagonal stiffeners was found not to buckle under the load.