The present paper deals with the thickness optimization of shells of revolution of various shapes and loads. The functional to be minimized is the potential energy of strain or some specified displacement of the shell, under the isoperimetric condition regarding its material volume. The problem formulation is based on the membrane theory of thin shells. Whenever possible the solution of particular problems is sought analytically using the calculus of variations. This permits us to judge what is the role of the input parameters and design variables on the final solution and to improve final understanding of the problem under consideration.