In calculating axisymmetric composite shell structures, the basic interest is in estimating the forces in the region of the joint by direct numerical methods or analytically. For their determination by the Fourier method, in combination with analytical methods, a cumbersome algorithm has been constructed on the basis of general solution of the equations of individual elements of the composite structure taken in one form or another. This algorithm may be considerably simplified if functions with properties similar to the properties of the well-known Krylov girder functions are chosen as the linearly independent solutions of the resolving equations of the given elements. In the present work, a differentiation rule of such functions is established for a cylindrical shell and an annular plate, and a simple algorithm is proposed for constructing the Cauchy matrix of the corresponding canonical systems of equations. The given algorithm allows the junction forces to be determined from the load in terms of the zero and first harmonics of its expansion in terms of the azimuthal coordinate in closed form and permits their analysis.