The bulk of cosmic rays of up to about 100 TeV are thought to be accel
erated by the first-order Fermi mechanism at supernova shocks, produci
ng a power-law spectrum. Both electrons and protons should be accelera
ted, but their ratio on acceleration is not well known. Recently, the
EGRET instrument on the Compton Gamma Ray Observatory has observed sup
ernova remnants IC 443 and gamma Cygni at GeV energies. On the assumpt
ion that the observed gamma-rays are produced by accelerated particles
in the remnants (rather than, for example, from a central compact obj
ect), we model the contributions from pion production, bremsstrahlung,
and inverse Compton scattering on the cosmic microwave, diffuse galac
tic, and locally produced radiation fields. In the case of the same sp
ectral index for both electrons and nuclei and a cutoff at 80 TeV, we
find that a spectral index of accelerated particles that is close to 2
.4 and a ratio of electrons to protons in the range 0.2-0.3 give a goo
d fit to the observed spectra. For lower cutoff energies, flatter spec
tra are possible. We also investigate the case in which the electron s
pectrum is steeper than that of nuclei. We discuss the implications of
our results for observations at air shower energies, and for the prop
agation of cosmic rays.