The paper is concerned with a curved triangular finite shell element, which represents the rigid-body motions exactly and assures convergence in energy. The stiffness matrix is derived in a general way that is valid for all mathematical models which accept Kirchhoff's assumption. A numerical example is presented to indicate the quality of results that can be obtained with 9 or 18 degrees of freedom at each meshpoint and basic functions of classes C1 or C2.