For the simulation and optimization of large-scale chemical processes, the overall computing time is often dominated by the time needed to solve a large sparse system of linear equations. We describe here a parallel frontal solver which can significantly reduce the wallclock time required to solve these linear equation systems using parallel/vector supercomputers. The algorithm exploits both multiprocessing and vector processing by using a multifrontal-type approach in which frontal elimination is used for the partial factorization of each front. The algorithm is based on a bordered block-diagonal matrix form and thus its performance depends on the extent to which this form can be obtained. Results on several large scale process simulation and optimization problems are presented, with emphasis on the effect of different matrix reorderings to achieve bordered block-diagonal form.