The most general analysis to date of X-ray data for the mass determination of the Coma Cluster is reported. The preferred model is one in which the mass distribution follows the distribution of the optical light. The total virial mass within 5/h50 Mpc is (1.85 + or - 0.24) x 10 to the 15th/h50 solar mass, and the mass-to-light ratio is 165 + or - 25 h50 in solar units. For these models the range in total mass is larger at (1.1-3.0) x 10 to the 15th/h50 solar masses, and the mass-to-light ratio varies from 90 h50 to 250 h50. The ratio of virial mass to X-ray emitting gas mass seems to decrease with radius from the cluster center. 26 references.