Finite element meshes based on completely overlapping covers are currently used as mathematical meshes in Numerical Manifold Method (NMM). The decline of calculation accuracy at some key parts is caused by the mismatch between physical meshes and mathematical meshes. In view of this, NMM with partially overlapping covers is presented for the first time. The method  adopts an analysis mode mainly concerning independent covers, and the continuity between the independent covers is kept by a small partially overlapping region. Thus NMM with completely overlapping covers is extended to the method of covers in a general meaning. Rectangular covers are preliminarily researched. The forms and formulas of partially overlapping covers are derived conveniently from completely overlapping covers by using freedom constraint among nodes of a single rectangular mathematical mesh. Finally, the validity and accuracy of the new NMM are demonstrated by an example.