Abstract: This paper is devoted to the development of a new meshless method based on a new approximation of shape function. In part 1 of this work, the analysis of results computed by the reproducing kernel particle method reveals that the support size of kernel function is a sensitive parameter in computing a violent displacement field. In order to solve this problem, an approximation method for constructing shape function is presented in part 2. The sensibility of kernel function support size can be weakened effectively in a computation of violent field by this method. A numerical example is given and comparison with the reproducing kernel particle method is made. It is shown that the method is stable in computation. One disadvantage of the method, however, is its high computational cost which needs further improvement.