Abstract: By means of the Fourier series expansion,an approximate analytical propagation equation of flattened Gaussian beams(FGBs) passing through an apertured paraxial ABCD optical system is derived,and illustr ated with numerical examples,when the transmissivity of the aperture is T(x)=cos(Ωx). The hard-edged aperture can be regarded as a special case of Ω=0. Numerical calculations results obtained by the straightforward integration of the Collins formula and our analytical equation are given,showing a good consistency within a small error range.