Abstract: The numerical manifold method(NMM) is widely applied to solve both continuous and discontinuous problems in solid mechanics with high efficiency.At the same time,the n-sided elements(n>4) are also very attractive due to their greater flexibility in meshing and higher efficiency in materials modeling,compared with the frequently used triangular and quadrilateral elements.To take advantage of the special feature that the mathematical cover system is independent of the physical domain in the NMM,in the present paper,the NMM is applied to solve 2-D elastostatic problems based on regular hexagonal(honeycomb) elements.Our results show that the accuracy on hexagonal elements is very close to that on regular quadrilateral elements but much higher than that on regular triangular elements.