A non-steady-state theoretical and mathematical model and a complex of computer codes have been developed for modeling a high-power double-pass explosively pumped photo-dissociation iodine laser (EPDL) with phase conjunction (PC) at SBS. The model and the complex of codes taking into account 3D of space consist of two blocks. The first block is devoted to detailed modeling of the SBS mirror consisting of an angular selector of Stokes radiation, an ordered raster of small diffraction lenses, a main focusing lens, and a SBS cell. The second block describes the dynamics of radiation in the laser system as a whole with using SBS mirror parameters calculated in the first block. The model takes into account parasitic reflections of laser radiation from the elements of the optical scheme, intrinsic amplified spontaneous emission of the amplifiers, radiation losses in the optical path, non-uniformity of gain, and radiation refraction on optical non-uniformaties of gain, and radiation refraction on optical non-uniformities of the active medium caused by a shock wave. As a result of calculations an optimal configuration of the SBS mirror has been determined, possessing unique properties if compared to the existing specimens of the SBS mirrors. It stably gives a nearly ideal quality of PC at any level of SBS saturation, i.e. any reflection coefficient that is confirmed by experimental laboratory investigations. Modeling of the laser system as a whole at working mixture 25 Torr C3F7I+125 Torr Xe and amplifier aperture 15 cm has been shown a good agreement of calculated results with available experimental data in energy, time dependence of power and Strehl number of output radiation. The considered EPDL has output energy of about 400 J and brightness of about 1012 J/ster. It is shown that parasitic reflections of laser radiation from the ends of amplifiers and elements of the optical scheme with a coefficient exceeding 10-7 considerably decrease the brightness of EPDL.