Summary: A parallel unstructured finite element (FE) reacting flow solver designed for message passing MIMD computers is described. This implementation employs automated partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global FE equations, and parallel Krylov subspace iterative solvers. In this paper, a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These issues include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured Krylov iterative solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics and single-node CPU performance on parallel performance. Results are presented for example FE heat transfer, fluid flow and full reacting flow applications on a 1024 processor nCUBE 2 hypercube and a 1904 processor Intel Paragon. Results indicate that very high computational rates and high scaled efficiencies can be achieved for large problems despite the use of sparse matrix data structures and the required unstructured data communication.