The electronic structures and optical properties, the atomic population, bond lengths, band structures and density of states (DOS) of undoped and doped rare earth elements (Y, La) in γ-Si3N4 have been calculated by means of plane wave pseudo-potential method (PWP) with generalized gradient approximation (GGA). The gap after doping will decrease and enables the formation of new semiconductor，which affords to help finding new semiconductor. We researched optical properties after doping of rare earth elements (Y, La), and found that the static dielectric constant of doped γ-Si3N4 is much higher than that of the undoped material，which may serve as new dielectric and refractive material，and may have special applications in certain optical devices.