Abstract: Numerical manifold method (NMM) is a very flexible numerical method which contains and combines finite element method (FEM) and discontinuous deformation analysis (DDA).High-order numerical manifold method can be constructed by increasing the order of the weight function.This method often needs to configure the appropriate edge nodes along the element boundary, the emergence of these nodes increase the complexity of pre-processing, especially for large and complex spatial problems.On the other hand, the level of approximation of NMM can be improved by splitting the elements into smaller ones (known as h-refinement).With regard to the h-refinement, a cover refinement strategy is necessary to overcome the singularity of the stress when simulating crack propagation in NMM.One traditional solution is to refine the entire mesh which can lead to a significant decrease in the computational efficiency.In this paper analysis-suitable T-spline is introduced into NMM and regular rectangular meshes are used as the mathematical cover system.Specifically, analysis-suitable T-spline is linearly independent, forms a partition of unity, and can be locally refined which make it meet the demands of both design and analysis.The basis function of analysis-suitable T-spline is adopted as the weight function in NMM to construct high-order NMM and make the local refinement for feasible adaptive procedure.Two numerical examples are given to demonstrate the accuracy and efficiency of the proposed method and the results show that the higher order AS T-spline based NMM shows higher accuracies when solving both continuous and discontinuous problems.Furthermore, the local mesh refinement using analysis-suitable T-spline reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.