This paper presents an analysis of the aeroelastic galloping of an elastically mounted square cross section in a free stream. The classic quasi-steady model [1] is used as a starting point. From this, the relevant time scales and dimensionless groups of the problem are derived. The time scale analysis shows that the mechanism of frequency selection by the oscillating system changes for heavy and light bodies. Results from direct numerical simulations are presented and compared against results from the simplified quasi-steady model, showing that the quasi-steady is quantitatively valid for heavy bodies, and at least generally qualitatively valid for light bodies. Results of experiments on light bodies also show this general qualitative agreement. However, there are also regimes of nonlinear interaction between the galloping and vortex shedding that the simplified model cannot capture.