A meshless local discontinuous Petrov-Galerkin (MLDPG)method based on the local symmetric weak form(LSWF)is presented with the application to blasting problems.The derivation is similar to that of mesh-based Runge-Kutta Discontinuous Galerkin(RKDG)method.The solutions are reproduced in a set of overlapped spherical sub-domains.and the test functions are employed from a partition of unlty of the lpeal basis functions.There is no need of any traditional nonoverlapping mesh either for lpeal approximation purpose or for Galerkin integration purpose in the presented method.The resulting MLDPG method is a meshless.stable.high-order accurate and highly parallelizable scheme which inherits both the advantages of RKDG and meshless method (MM),and it can handle the problems with extremely complicated physics and geometries easily.Three numerical exampies of the one-dimensional Sod shock-tube problem.the blast-wave problem and the Woodward-Cpiella interacting shock wave problem are given.All the numerical results are in good agreement with the closed solutions.The higher-order MLDPG schemes can reproduce more accurate solution than the lower-order schemes.