This study examined different constellation configurations to determine their suitability for the Mars Network. Some variations on the baseline case of four circular orbits were initially studied. Eccentric orbits were then used to determine their effects on several figures of merit that were selected as representative of the design goals. It was eventually found that the use of eccentric orbits in combination with circular orbits can improve aspects of some navigation and communication figures of merit. The ability to use orbits at different inclinations helps smooth coverage over the middle and upper latitudes for these figures of merit. This configuration has more variability than one consisting of circular orbits, so the occurrence of unfavorable arrangements also results in degradation of some figures of merit. Some cases were used which improved different figures of merit, so a solution could be chosen depending on specified requirements.