The nonlinear dynamics of the cylindrically symmetric high—frequency discharge produced by а circular polarized electric field is considered. Three main stages of discharge evolution are analyzed by computer simulation. These stages are е following: (i) self—acceleratlng avalanche—like process which develops up to plasma density maximum corresponding to «geometric» resonance of the plasma cylinder; (ii) diffusion propagation of the fast ionization wave which contains the plasma resonance region at its leading edge; (iii) transition to the steady—state. The sharpening regimes for the field amplitude and plasma density profiles in the vicinity of the plasma resonance point at the axes are analyzed. The arising dynamic structures are found to be in a good agreement with the self-similar solution defined for the electric field and plasma density nonlinear equation set.