Titanium and its alloys are used in numerous applications due to their mechanical properties and corrosion resistance. However, their use in relation to oxygen applications has been limited because pure titanium and an alloy (Ti-6Al-4V) are extremely flammable in pure oxygen at pressures below atmospheric. Research has demonstrated that titanium, unlike many other metals, can ignite and sustain burning in oxygen concentrations less than 100% (with nitrogen). This behavior is likely due to its ability to form not only oxides, like most metals, but also nitrides through nitrogen reactions. The specific regions of titanium and Ti-6Al-4V flammability, when the oxygen concentration is less than 100%, however, are not documented for either normal- or reduced-gravity conditions. This work uses the concept of the oxygen index, historically used to study the compatibility of nonmetals with oxygen, to investigate the flammability of titanium and Ti-6Al-4V under two gravity regimes; we also identify flammability regions using the combustion test for metals as outlined in ASTM G94-22. We describe the specific experiments performed and the experimental conditions evaluated; the methodology used; the results of the experiments, including the test sample burn lengths; the regression rates of the melting interface (assessed both visually and with an ultrasonic measurement system); and the regions of flammability as defined by ASTM G94-22 for titanium and a Ti-6Al-4V alloy using the concept of the oxygen index.