The vaporization of a fuel cloud in an infinite, quiescent atmosphere is examined. A single global parameter which characterizes the vaporization process, and is related to the ratio of the thickness of a vaporization wave to the cloud radius, is identified. Typical fuel sprays correspond to very small (e.g., 104) values of this parameter. An asymptotic analysis of the cloud, predicated on this parameter being small, shows that the cloud and its environment are divided into four distinct regions: (1) the saturated, non-vaporizing cloud interior; (2) a quasi-steady vaporization wave located at the edge of the cloud and propagating radially inward; (3) a quasi-steady (”inner”) region located outside the cloud but in its vicinity and (4) an unsteady (”outer”) region located far from the cloud. A phenomenological model of the vaporization wave is also presented, along with sample calculations using typical cloud data.