Laser beams generated from high-magnification on-axis unstable resonators using hard-edged axial scraper mirrors and output couplers consisting of axial spot reflectors typically have an annular distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We employ a new model, based on the flattened Gaussian beam (FGB) concept, to describe the propagation of such annular near-field beams. The superposition of two FGBs, whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order), is used to analyze the output beam intensity profile along the propagation axis. We apply this model to characterize the output beams of copper vapour lasers employing unstable resonators of different magnifications (M = 80, 200, and 400). We show that once the model is fitted to the beam intensity profile at any two positions along the axis of propagation, it can be used to predict the beam shape at any position.