  The spectra of high-energy protons and nuclei accelerated by supernova
remnant shocks are calculated taking into account magnetic field amplification
and Alfvenic drift both upstream and downstream of the shock for different
types of supernova remnants during their evolution. The maximum energy of
accelerated particles may reach $5\cdot10^{18}$ eV for Fe ions in Type IIb
SNRs. The calculated energy spectrum of cosmic rays after propagation through
the Galaxy is in good agreement with the spectrum measured at the Earth.
