A preliminary study is made of the h-adaptive refinement scheme for the Natural Element Method(NEM). The solution error is estimated by using the ZZ error estimator which is based on the recovery stress filed acquired through the MLS/NNI stress recovery scheme according to the character of the NEM. Then new nodes are inserted automatically according to the error distribution information acquired. With the process of the adaptive analysis

the solution error reduced and the distribution of the error tend to be uniform. In numerical analysis

there is mainly two sources of error

namely the interpolation error and integration error

with the increase in nodes

the size of Delaunay triangle decreases and the stress tend to be linear

so the interpolation error and integration error decreases accordingly. In the process of adaptive analysis

solution errors can be reduced and the accuracy improved. The Voronoi tessellation is needed in the NEM analysis

the refinement scheme presented is just involved in the local adjustment of the Delaunay Tessellation. The implementation of adaptive process is effective and efficient. Numerical examples show that the adaptive scheme is successful and NEM is especially suitable for h-adaptive analysis.