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A parallel computational implementation of a meshfree method—the reproducing kernel particle method (RKPM)—is used for 3-D implicit CFD analysis. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. Using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite-element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions. This technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations, many of which involve inherently serial steps; this is important, because the expense of meshfree computations makes parallelization crucial for large-size problems. The performance of the parallelization technique and the accuracy of the implicit CFD algorithm are demonstrated in two example problems. [Copyright &y& Elsevier]