AbstractBased on the modified principle of potential energy, three triangular thin‐plate elements with nine degrees of freedom (LZ1, LZ2 and LZ3) are derived by using compatibility conditions for nodal deflection at each node and generalized compatibility conditions for average deflection and average normal slope along each side of the element. These generalized conforming elements are low‐order and high‐precision elements which pass the patch test. When overall considerations of accuracy, simplicity and reliability are taken into account, these new elements are the best 9‐DOF triangular thin‐plate elements currently