  The processes responsible for the broad-band radiation of the young supernova
remnant Cas A are explored using a new code which is designed for a detailed
treatment of the diffusive shock acceleration of particles in nonlinear regime.
The model is based on spherically symmetric hydrodynamic equations complemented
with transport equations for relativistic particles. Electrons, protons and the
oxygen ions accelerated by forward and reverse shocks are included in the
numerical calculations. We show that the available multi-wavelength
observations in the radio, X-ray and gamma-ray bands can be best explained by
invoking particle acceleration by both forward and reversed shocks. Although
the TeV gamma-ray observations can be interpreted by interactions of both
accelerated electrons and protons/ions, the measurements by Fermi LAT at
energies below 1 GeV give a tentative preference to the hadronic origin of
gamma-rays. Then, the acceleration efficiency in this source, despite the
previous claims, should be very high; 25% of the explosion energy (or
approximately $3\cdot 10^{50}$ erg) should already be converted to cosmic rays,
mainly by the forward shock. At the same time, the model calculations do not
provide extension of the maximum energy of accelerated protons beyond 100 TeV.
In this model, the acceleration of electrons is dominated by the reverse shock;
the required $10^{48}$ erg can be achieved under the assumption that the
injection of electrons (positrons) is supported by the radioactive decay of
$^{44}$Ti.
