Amplified spontaneous emission of laser media having a spherical or disk shape is numerically analyzed. Some properties are discussed and a comparison with linear systems is made. Analytical approximations, for the case of high pumping rates and high efficiency, are obtained. Energy level schemes of dye systems are used in the analysis and in the numerical calculations. A coupled set of radiative transfer and rate equations is solved under quasi-steady-state conditions. The model takes into account the fluorescence spectrum and gain saturation effects with radially symmetric distributions of the active dye molecular densities. As a comparison, the numerical examples also include an H2O system which is relevant in astrophysics.