The propagation of light pulses within waveguide Bragg gratings is investigated. The exact mathematical solution of the problem for the grating with rectangular groove shape is considered. The solution is valid for arbitrary
grating amplitude and length both in the vicinity and far from Bragg wavelength. For this solution the distribution of field amplitudes within the grating, its reflectivity and the structure of resonances are studied. The
effects of light pulse broadening, shape transformation and time delay due to interaction with the waveguide Bragg grating are analyzed using numerical simulations.