Parallel computation of blood flow in a 1D model of human arterial network has been carried out employing a Taylor Galerkin finite element method. Message passing interface libraries have been used on Origin 2000 SGI machine. A Greedy strategy for load-distribution has been devised and data-flow graphs necessary for parallelization have been generated. The performance of parallel implementation measured in terms of speedup and efficiency factors is found to be good. Further, the parallel code is used in simulating the propagation of pressure and velocity waveforms in our 1D arterial model for two different inflow pressure pulses. Also, the influence of consideration of terminal resistance on pressure and velocity waveforms have been analyzed