Abstract: The elliptical flattened Gaussian beam (EFGB) is defined by using tensor method. The propagation formula and corresponding tensor ABCD law of EFGB passing through nonsymmetrical paraxial optical system is derived through vector integration. By using this formula, the propagation characteristics of EFGB through free-space are calculated and discussed. The results show that the propagation property is very different from those of circular flattened Gaussian beam or elliptical Gaussian beam, and is dependent on the order N. In the near field, the intensity distribution remains flat. With the increase of propagation distance, the flattened part degenerates. In the far field, EFGB tends to be elliptical Gaussian beam. Furthermore, beam spots of coupled EFGB rotate with propagation distance z.