Recent calculations of particle acceleration in supernova remnants (SN
Rs) are used to estimate the associated gamma-ray production. For sour
ce spectra which are power-laws in momentum (or rigidity) the producti
on efficiency of gamma-rays with energy E(gamma) > 100 MeV is shown to
be about a factor 2-3 lower than the value conventionally used for th
e interstellar medium and to depend only weakly on the spectral index
of the power-law (in the range expected). Because the energy transferr
ed to accelerated particles is rather tightly constrained by the total
Galactic cosmic ray power, if SNRs are the main source of Galactic co
smic rays, this leads to an almost model-independent prediction of the
SNR gamma-ray luminosity in the band E(gamma) > 100 MeV. A detailed d
iscussion of instrumental sensitivities and backgrounds shows that det
ection of SNRs in the E(gamma) > 100 MeV band with, for example, the E
nergetic Gamma Ray Experiment Telescope (EGRET) will be difficult, but
should not be impossible. However, and significantly, the prospects l
ook much better in the TeV band accessible to modern imaging atmospher
ic Cherenkov telescopes. It should be possible to detect SNRs out to d
istances of several kpc if the region of the ISM into which they are e
xpanding has a high enough density (n > 0.1 cm-3) so that their gamma-
ray luminosity is high enough. Finally, it is pointed out that existin
g and planned air-shower arrays can place important limits on the exte
nsion of the accelerated particle spectra in SNRs to energies above 10
0 TeV. In conjunction with spectral measurements in the TeV region and
detections or upper limits in the 100 MeV band this could provide a c
rucial test of current theories of particle acceleration in SNRs.