On the foundation of the initial parameter formulae of elastic circular ring with constant flexural rigidity,using the stepped reduction method, suggested in[2],we investigate the bending problem of non-homogeneous variable thickness elastic circular ring under arbitrarily distributed loads and obtain the general solution of this problem which is also suitable for the corresponding problem of non-homogeneous variable thickness cylindrical arch.In the end, an example is carried out to examine the gained formulae and assure the exactness of this method.