A review is given of the results from one and two‐dimensional computer heat flow models developed to investigate the effect of high intensity stationary heat fluxes, e.q. such as those achieved via laser radiation, on the important surface melting and subsequent solidification variables of different substrates. The problem considered is the rapid melting and solidification of the surface layer of a semi‐infinite solid subjected to step function stationary uniform and Gaussian heat flux distributions over a circular region on its bounding surface. Criteria are developed that specify conditions under which the surface of a substrate would melt and superheat, and conditions under which the simpler one‐dimensional heat flow analysis is applicable. General trends established relate the important melting and solidification parameters to absorbed heat flux, radius of the circular region and time. Some preliminary experimental observations are presented from surface melted Al‐4.5% Cu specimens.