The computational efficiency of a reservoir simulator-MARS-that is heavily used in Saudi Aramco, was significantly enhanced by improving the vectorization, parallelization and a key algorithm of the simulator. In particular, a state-of-the-art parallel linear equation solver was developed and implemented in the simulator. This new solver ran three to five times faster than the existing solvers. With the new solver and the other improvements in the simulator, the optimized code ran 1.3 to 1.8 times faster than the original code on a single processor and more than four times faster on four processors of Cray-2 supercomputer for typical Saudi Aramco reservoir models. This translates into great savings for the company since it, in effect, creates additional computational resources at no additional cost and improves the reservoir engineer`s productivity by shortening the job turnaround time.