Generally

a finite element mesh or a regular mesh is used as the mathematical covering system in the numerical manifold method（NMM）. The advantage of the regular mesh is that it has no requirement to conform to the boundary of the solution domain and various discontinuities. In this paper

the regular rectangular mesh was used as the mathematical mesh in NMM

and the analysis-suitable T-spline was introduced into NMM to realize the local refinement. As the analysis-suitable T-spline was defined over a mildly restricted T-mesh

it presents many important mathematical properties

such as linear independence

partition of unity and highly localized refinement capability. However

after an analysis-suitable T-mesh was locally refined

the generated new T-spline was not analysis-suitable. Therefore

a simple local refinement algorithm was developed in this paper to make sure that the refined mathematical mesh was still analysis-suitable. Moreover

the results from numerical examples show that the algorithm has strong applicability in large-stress gradient areas such as stress concentration area and crack tips.