The subject how to characterize high-power lasers is studied. The flattened Gaussian beam (FGB) is taken as an illustrative example, and the propagation of FGBs passing through unapertured and apertured paraxial ABCD optical systems is expressed in the analytical form. The beam characteristic parameters including the beam propagation factor (M² factor), kurtosis (K parameter) and power in the bucket (PIB) of FGBs are given and analyzed physically. Finally, it is pointed out that from a practical point of view the beam control of high-power lasers means that the power/energy focusability on the target, temporal and spatial profile, pointing stability and sustainability of beams should satisfy application requirements. It is a challenging subject in modern optics and laser technology.