The finite element analysis of shells of revolution including circular cylindrical shells under the axisymmetric loading was first carried out by Grafton and Strome. Percy et al.elaborated the extension to the case of non-axisymmetric loading, which was suggested by Grafton and Strome. In these approaches the displacement field in the conical frusta element was used, which was expanded into Fourier series in the circumferential direction and represented by lower order polynomials in the axial direction. In new discrete elements for circular cylindrical shells proposed in this paper, linear shape functions are assumed in the axial direction and the stiffness matrices are made by the combined use of the finite difference approximation and the finite element approach with the partial approximation. The stiffness matrices can be given in the explicit form and the number of unknown variables on the nodal line corresponding to a term of Fourier series expansion is 3, while 4 in the conventional finite element method. In spite of the above simplicity the solution obtained by using these new discrete elements is extremely good both in elastic and elasto-plastic analysis, that will be proved by several numerical results on the fundamental problems in linear elastic and limit load analysis of circular cylindrical shells.