The effective use of modeling techniques in the study of free-burning fires requires more knowledge of the essential scaling laws than has hitherto been available. These laws are developed for a stationary area or 'mass' fire by the methods of dimensional analysis. If fires are burning in calm air, geometric similarity is determined by only one dimensionless group which may be defined as a buoyancy number. For fires burning in a wind stream, geometric similarity is determined by two dimensionless groups - a buoyancy number and a Froude number. Additional groups from the dimensional analysis show how variables such as lengths, times, accelerations, and temperatures scale. A hypothetical model fire, based partly on estimates and partly on observations of laboratory fires, illustrates how a relatively simple model could be used to predict the characteristics of a large stationary mass fire.