In this paper, the authors study parallel algorithms for meshless numerical simulation of system linear equations $[M]\{\ddot{u}\}+[K]\{u\}=\{F\}$ derived from elastic body problems, where $M$ is the mass matrix, $K$ is the stiffness matrix, $F$ is the vector of external force and $\ddot{u}$ is the acceleration vector. They discuss the parallel bucket search method for node search and the parallel geometry search method for sample point search. The parallel computation of meshless shape functions and their derivatives, the parallel treatment of boundary conditions and the parallel solution of a system of equations by a preconditioned conjugate gradient method, are addressed in detail. To deal with the load balance of CPU in parallel computing of meshless methods, an METIS (multilevel partitioning algorithm) is presented. Numerical experiments on plane inelastic problems are performed. The authors draw the conclusion that the larger the scale of the problem, the higher the parallel efficiency.