A nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is employed to investigate the properties of SNR RX J1713.7-3946. Observations of the non-thermal radio and X-ray emission spectra as well as the H.E.S.S. measurements of the very high energy gamma-ray emission are used to constrain the astronomical and CR acceleration parameters of the system. It is argued that RX J1713.7-3946 is a core collapse supernova (SN) of type II/Ib with a massive progenitor, has an age of ~1600 yr and is at a distance of ~1 kpc. It is in addition assumed that the CR injection/acceleration takes place uniformly across the shock surface for this kind of core collapse SNR. The theory gives a consistent description for all the existing observational data, including the non-detection of thermal X-rays and the spatial correlation of the X-ray and gamma-ray emission in the remnant. Specifically it is shown that an efficient production of nuclear CRs, leading to strong shock modification and a large downstream magnetic field strength B_d ~140 mkG can reproduce in detail the observed synchrotron emission from radio to X-ray frequencies together with the gamma-ray spectral characteristics as observed by the H.E.S.S. telescopes. The calculations are consistent with RX J1713.7-3946 being an efficient source of nuclear cosmic rays.