AbstractA triangular flat facet finite element for the analysis of general thin shells is presented. It is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices, thereby easily meeting the requirements of standard commercial computer programs. The theoretical development is based on a variational principle which allows a direct formulation of the element stiffness matrix, without inversion, and which permits considerable simplification of the mathematical formulation. The new flat facet element generally produces more accurate numerical results than those obtained in earlier related work. It also offers a possible basis for constructing an improved curved approximation to a shell surface and for further developments in connection with applications involving geometric non‐linearit