Abstract: It is known that usually the degree of sharpness (or flatness) of beam intensity distribution is described by the kurtosis parameter (K parameter).Taking cosh-Gaussian (ChG),Bessel-modulated Gaussian (QBG),and flattened Gaussian (FG) beams as three illustrative examples,detailed numerical calculations and physical interpretations were given.It is shown that the K parameter is suited essentially to characterize the sharpness of the bell-shape beam profile,but not applicable to beams with large diffraction sidelobes,large intensity modulations,and beams with central shadow.