Abstract：Abstract：The meshless manifold method is utilized to analyze transient deformations of the elastodynamics，especially，with discontinuity in the solving domain. The shape function is built with the method by the partition of unity and the finite cover technology，so the shape function cannot be effected by discontinuity in the domain to treat continuous and discontinuous dynamics problem easily. To local problems，the shape functions are built more effectively than other method. So the method can avoid the disadvantages in other meshless methods in which the tip of the discontinuous crack isn¢t considered. The approximation functions will not be influenced by the discontinuity in the solving domain if finite cover technology is employed in the method，which can overcome some difficulties when the problems are solved with the meshless methods. When the meshless manifold method is utilized to analyze the elastodynamics，the method is divided into the major two parts：the discrete space of the domain is used to the partition of unity，which the present method void to mesh element and refine element. So the method has good continuity in the area of the computing stress for element-free of the analysis problem. The Newmark methods is used for the time integration scheme. The scheme is a widely direct integration method. The local weak formulation of the dynamic partial differential equation for elastic is derived from the method of weighted residuals(MWR). At last，the validity and accuracy of the presented meshless manifold method solution are illustrated by the 2D plate of the elastodynamics. The meshless manifold method results show that the stresses and the displacements at the critical point agree well with those obtained from the analytical solution.
