A theoretical model is developed which clarifies the reason for the appearance of a magnetic and/or optical anisotropy in garnets under illumination with linearly polarized light. The model is base on the calculation of the occupancies’ kinetics of anisotropic impurity centers localized in different garnet sublattices. A comparison of experimental data for the magnetic yttrium-iron garnet doped with cobalt (YIG:Co) and the non-magnetic Ca3Mn2Ge3O12 (CaMnGe) garnet to the results of the model is performed which leads to a good agreement.