The Finite-pointset method (FPM) is a mesh-free Lagrangian method. In this article, we discuss issues in parallelizing the FPM on distributed memory architecture. The Message Passing Interface (MPI) standard library is used for communication. We have developed algorithms to achieve fine-grained parallelism. Issues relating to Load Balancing and communication between processors have been addressed. A parallel version of the BiCGSTAB linear solver is implemented. The efficiency and speedup results for the parallel linear solver, used in conjunction with our load-balancing technique, are presented. © 2011 Taylor & Francis.