Abstract: The analytical expressions for the mode coefficients and M2-factor of partially coherent flat-topped beams which can be combined by independent Hermite-Gaussian beams have been derived.The mode decomposition and mode composition of partially coherent flat-topped beams have been analyzed.The basis Gaussian mode decreases and the M2-factor increases with the beam order M and the parameter w0/ν0 increasing.The M2-factor and the rectangular shape of the flat-topped beams combined by the independent Hermite-Gaussian beams can not be obtained at the same time.If an approach rectangular shape of the intensity distribution of partially coherent flat-topped beams is desired,the M2-factor must be large.If the small value of M2-factor is required,the strictly rectangular shape of the intensity distribution can not be obtained.In many practical cases,the partially coherent flat-topped beams can be combined by the superposition of the independent Hermite-Gaussian beams with the proper choice of the beam waist and the power content.