Abstract: The present paper discusses a method of optimal design of the shallow shell, with double curvature on the elastic foundation, Substantially we take the initial flexural function as the control function or design variable which will be found and the potential energy of the eternal loads as the criterion of quality of the optimal design of the shallow shell with double curvature, therefore the functional of the potential energy will be aim function, The optimal conditions and the isoperimetric conditions belong to the constrained conditions, thus we obtain the necessary conditions of the optimal design for the given problems, at the same time the conjugate function is introduced, then the problems are reduced to the solutions of two boundary value problems for the differential equation of conjugate function and tba initial fleeural function.