  The nonlinear kinetic model of cosmic ray (CR) acceleration in supernova
remnants (SNRs) is used to describe the relevant properties of Cassiopeia A
(Cas A). In order to reproduce the SNR's observed size, expansion rate and
thermal X-ray emission we employ a piecewise homogeneous model for the
progenitor's circumstellar medium developed by Borkowski et al. (1996). It
consists of a tenuous inner wind bubble, a dense shell of swept-up red
supergiant wind material, and a subsequent red supergiant wind region. A quite
large SNR interior magnetic field B_d approx 1 mG is required to give a good
fit for the radio and X-ray synchrotron emission. The steep radio spectrum is
consistent with efficient proton acceleration which produces a significant
shock modification and leads to a steep electron spectrum at energies E_e < 1
GeV. The calculated integral gamma-ray flux from Cas A, F propto E_gamma^-1, is
dominated by pi^0-decay gamma-rays due to relativistic protons. It extends up
to roughly 30 TeV if CR diffusion is as strong as the Bohm limit. At TeV
energies it satisfactorily agrees with the value 5.8 x 10^-13 cm^-2 s^-1
detected by the HEGRA collaboration.
