The amplitude of plasma waves, excited by the resonant sequence of electron bunches, saturates after passage of some number of bunches. This behavior was observed and simulated, using particle-in-cell code, but was not completely explained yet. Our study of this behavior was carried out via computer simulation, using modified PDP3 code − 2D3V PIC code for axially symmetric geometry and relativistic collisionless plasma. Simulation demonstrated that amplitude saturation was caused by the plasma pressing-out from the area of the most intensive wake field. This hypothesis has been verified by the obtained electrical and magnetic field spectra, temperature and density maps and density profile for various simulation times.