Abstract: Two versions of area coordinate systems for quadrilateral elements (QAC-I and QAC-II) have been developed. The QAC-I contains four coordinate components (L1, L2, L3, L4), among which only two are independent. The QAC-II contains only two independent coordinate components (Z1, Z2). These area coordinate systems provide the theoretical bases for the construction of new quadrilateral element models insensitive to mesh distortion. In this paper, the third version of area coordinate systems for quadrilateral elements (QAC-III) with two coordinate components (T1, T2) is systematically established. This new QAC-III not only retains the most important advantages of both QAC-I and QAC-II, but also possesses other distinguished characters: 1) it is a natural coordinate system; 2) it keeps simple linear relationship with the Cartesian coordinate system; 3) it contains only two coordinate components; 4) the shape function developed has a simpler form; 5) it can be directly applied to curved quadrilateral elements; 6) three version I , II and III can be used in a mixed form to give the optimal results.