Abstract：In meshless manifold method，finite cover technology is employed. The mathematical finite cover approximation theory is used to model cracks that lead to displacement discontinuity. The discontinuity is treated mathematically instead of empirically by the existing methods such as：(1) the diffraction method；(2) the transparency method；and (3) the see-through method. One cover of a node is divided into two irregular sub-covers when the meshless manifold method is used to model the discontinuity. However the method sometimes causes numerical errors at the tip of a crack. To improve the precision of the meshless manifold method，the enriched methods are introduced. The enrichment of solution of the meshless manifold method near the tip of a linear- elastic crack is achieved by expanding the basis functions with special functions. The validity and accuracy of the enriched meshless manifold method are illustrated by numerical examples.
