In the finite element analysis of curved structures such as circular arches and spherical shells, there are two types of method of analysis. In the first method these structures are idealized as assemblies of straight elements, which are straight beam elements for circular arches and conical frusta elements for spherical shells. (The ring type of elements is only considered in the analysis of shell structures.) In the second method curved finite elements are adopted which can represent the curved shape of the middle surface exactly, where the accuracy of obtained solutions are considerably improved in comparison with the first approach, however it requires a little complicated formulation. In this paper new discrete elemets for analysis of circular arches and spherical shells are proposed, which are very simple and efficient. Linear shape functions are assumed for all three displacement components. The membrane (or axial) stiffness matrix is made, following the convensional finite element procedure with the partial approximation, while the bending stiffness matrix is made by using the finite difference approximation. Both stiffness matrices can be obtained in the explicit form and the nodal variables have only translational components. Several numerical examples will be presented to show the efficiency of these new discrete elements.