The use of tensilely strained Ge nanomembranes as mid-infrared optical gain media is investigated. Biaxial tensile strain in Ge has the effect of lowering the direct energy bandgap relative to the fundamental indirect one, thereby increasing the internal quantum efficiency for light emission and allowing for the formation of population inversion, until at a strain of about 1.9% Ge is even converted into a direct-bandgap material. Gain calculations are presented showing that, already at strain levels of about 1.4% and above, Ge films can provide optical gain in the technologically important 2.12.5 m spectral region, with transparency carrier densities that can be readily achieved under realistic pumping conditions. Mechanically stressed Ge nanomembranes capable of accommodating the required strain levels are developed and used to demonstrate strong strain-enhanced photoluminescence. A detailed analysis of the high-strain emission spectra also demonstrates that the nanomembranes can be pumped above transparency, and confirms the prediction that biaxial-strain levels in excess of only 1.4% are required to obtain significant population inversion.