The focus of this research was the design, fabrication, and testing of an experimental non-premixed flame burner to determine the effect of gaseous flow parameters and flow geometry on the stability of methane/oxygen combustion. The non-premixed burner consisted of a horizontally mounted, rectangular combustion chamber with a single coaxial injector, capable of introducing reactants at a specified impingement angle. Gaseous oxygen was the primary flow and gaseous methane was the secondary flow. The non-premixed burner was equipped with optical windows on both sides of the chamber parallel to the axis of the flame, which allowed for clear viewing of the product flame. Ignition of the reactants was achieved by a retractable spark plug. Stability maps of the resultant diffusion flame were created for two different exit flow areas based upon oxidizer-to-fuel mass ratio, equivalence ratio, and primary reactant Reynolds numbers. The results showed that decreasing the primary flow area resulted in a more stable flame over a broader range of Reynolds numbers. For both flow areas tested, increasing Reynolds number resulted in a transition from a stable, anchored flame to a detached, unstable flame. As equivalence ratio approached unity, the diffusion flame become more unstable as well.