Abstract: It is always a question open to discuss that which kind of element is more optimal for the finite element analysis of membrane structures, the triangular finite element of constant stress or the curved triangular finite element with 6 nodes. This paper carries on the analysis of this problem. It first focuses on the format of the two kinds of finite elements, revealing some elemental differences on a displacement model, the geometry equation and stiffness matrix between the two elements. Then by typical numerical examples, their accuracy and efficiency in calculation are analyzed and compared. The study shows that: curved triangular elements are more comprehensive and closer to the mechanical performance of authentic membrane, compared with triangular finite elements of constant stress; also the former appear more advantageous on accuracy and efficiency of the calculation. Therefore, from a point of view on refined analysis, it is better to adopt curved triangular elements in calculation.