The process of the electromagnetic wave propagation in the nonlinear Bragg grating system has been numerically studied. The nonlinear Kerr materials were considered. The values of the cut-off frequencies were approximately estimated with the modification of the effective refractive index method. A Finite-Difference-Time-Domain method was used to analyze the periodic nonlinear structures and to investigate the multiple gap-soliton formation within the photonic bandgap of the Bragg grating. The possibility of propagation of the signal which frequency lies within the band gap of the periodical structure was demonstrated. The process of soliton tunneling in the nonlinear 2D Bragg grating has been investigated.