When applied to the blast wave formed by the explosion of a massive st
ar as a supernova (SN), the theory of diffusive particle acceleration
at shock fronts predicts a very high energy density in cosmic rays. Al
most immediately after particles begin to be injected into the process
, the cosmic ray pressure rises until comparable to the ram-pressure e
ncountered 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 acc
eleration 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 less than or similar to 1 of the energy avail
able at the shock front is converted into cosmic rays. Combining this
with the parameters describing the environment of the SN progenitor, a
s deduced from observations, and from more detailed modelling, we comp
ute the flux at Earth F(> 1 TeV) of photons of energy above 1 TeV. For
the relatively weak but nearby supernova SN1987A we predict F(> 1 TeV
) = 2 x 10(-13) photons s(-1) cm(-2) before the shock front encounters
the ring of dense matter seen by the Hubble Space Telescope. Subseque
ntly, the flux is expected to rise further. The medium around SN1993J
in M81 is thought to have a density profile rho proportional to tau(-3
/2), (with tau the distance from the point of explosion) for which we
predict a roughly constant flux of F(> 1 TeV) = 2 x 10(-12) photons s(
-1) cm(-2). Once the shock emerges into the region where rho proportio
nal to tau(-2), which is expected at larger distances, the flux should
decrease in proportion to t(-1). This object thus presents an interes
ting target for observation by telescopes which detect the Cerenkov li
ght emitted by the air showers from VHE photons. A detection would pro
vide observational confirmation of cosmic ray acceleration in supernov
ae.