This paper is concerned with finite-element analysis of thin elastic shells described by the Koiter-Sanders mathematical model. The middle surface of the shell is decomposed into curved finite triangular elements, which are mapped onto straight triangles in the plane of parameters of the surface. We show that with an appropriate approximation of the given surface, rigid-body motions may be represented exactly. Nine degrees of freedom are associated with each nodal point (the vertices of the elements) and the displacement functions fulfill the conditions of regularity required by Ritz’s method and assure convergence in energy. The derivation is quite general with respect to the geometry of the shell. A cylindrical shell analysis is presented as an illustrative numerical example.