On the Rytov approximation of light propagation in weak turbulent atmosphere and the fact that nondiffracting beams can be expanded in terms of plane waves,we present the propagation characterization of Mathieu-Gauss beams. The expression of Mathieu-Gauss beams which are propagation in weak turbulent atmosphere can be written as the product of four factors:a complex amplitude depending on the z coordinate only,a Gaussian beam,a factor of complex phase induced by atmospheric turbulence,and a complex scaled version of the transverse shape of the nondiffracting beam. The normalized axial irradiance distribution of Mathieu-Gauss beams as a function of the normalized propagation distance z=z/zR and the parameter γ=1[]2kρw0 which is propagation in atmospheric turbulence is same as that of this beams propagation in flee space.