  While the definitive detection of gamma-rays from known supernova remnants
(SNRs) remains elusive, the collection of unidentified EGRET sources that may
be associated with SNRs has motivated recent modelling of TeV emission from
these sources. Current theoretical models use power-law shock-accelerated
protons and electrons in their predictions of expected gamma-ray TeV fluxes
from those unidentified EGRET sources with remnant associations. In this paper,
we explore a more detailed non-linear shock acceleration model, which generates
non-thermal proton distributions and includes a self-consistent determination
of shock hydrodynamics. We obtain gamma-ray spectra for SNRs allowing for the
cessation of acceleration to high energies that is due to the finite ages and
sizes of remnants. Gamma-ray spectral cutoffs can be observed in the TeV range
for reasonable remnant parameters, and deviations from power-law behaviour are
found at all energies ranging from 1 MeV up to the cutoff. Correlated
observations by INTEGRAL, Whipple and other instruments may provide stringent
constraints to our understanding of supernova remnants.
