  When applied to the blast wave formed by the explosion of a massive star as a
supernova (SN), the theory of diffusive particle acceleration at shock fronts
predicts a very high energy density in cosmic rays. Almost immediately after
particles begin to be injected into the process, the cosmic ray pressure rises
until comparable to the ram-pressure encountered by the shock front. Those
supernovae which are observed in the radio band i.e., radio supernovae (RSNe),
provide direct evidence of particle acceleration in the form of synchrotron
emitting electrons. Furthermore, these objects are particularly interesting,
since they are usually surrounded by a relatively dense confining medium. The
acceleration of cosmic rays can then lead to the production of very high energy
(VHE) gamma-rays which arise from collisions between energetic particles and
target nuclei. We estimate the cosmic ray energy density assuming a fraction
$\phi\lesim1$ of the energy available at the shock front is converted into
cosmic rays. Combining this with the parameters describing the environment of
the SN progenitor, as deduced from observations, and from more detailed
modelling, we compute the flux at Earth $\tevflux$ of photons of energy above
$1\,$TeV. For the relatively weak but nearby supernova SN1987A we predict
$\tevflux=2\times10^{-13}\,\fluxunits$ before the shock front encounters the
ring of dense matter seen by the Hubble Space Telescope. Subsequently, the flux
is expected to rise further. The medium around SN1993J in M81 is thought to
have a density
