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A method is suggested for computing shells stiffened with beams. This described in stresses not, in the usual manner, in displacements. An arbitrary shell is considered. It was necessary to establish conditions inside the shell on the basis of the stress functions and the elastic interaction of the stiffening beams constituting the boundary conditions. Four conditions on each edge are available, ensuring the uniqueness of solution of the partial differential equation of the elliptical type from which the stress functions are obtained. In order to state the used as problem inside the region, stress functions are given by Lurye and Goldenweiser ([8], p. 37). They are completed by the present author with a particular integral of non-homogeneous equilibrium equations and compatibility conditions used in the elastic region for shells. Next it is shown that for cylindrical shells and rectangular plates, equations of the same type are obtained for the resolving function as in the case of solution in determination. The interaction of the beam with the shell displacements in the form of boundary conditions obtained is expressed by the author in the form of boundary conditions obtained from the equilibrium conditions of a beam loaded by the reactions of the shell, and from geometrical relations appearing in the case in which both parts constitute a monolithic structure. The application of the general equations is illustrated by way of an example of a cylindrical shell and a plate. The computation method is illustrated by a numerical example of a plate with elastic ribs. The results are presented graphically.