Abstract: Numerical Manifold Method (NMM) with covers of arbitrary shape is presented for the first time based on previous research of partially overlapping rectangular covers. The characteristics of this method are as follows covers with arbitrary shape are connected with each other through strips; it has a unique analysis mode mainly involving independent covers; the functions of the Partition of Unity(PU) are presented in a special way with strict interpolation properties. The fundamental forms of covers of arbitrary shape,as well as the realization method based on totally overlapping covers by using freedom constraint are given. Finally,the validity of the new method is demonstrated by a numerical example.

Key words: Numerical Manifold Method (NMM), covers of arbitrary shape, partially overlapping covers, Partition of Unity(PU)