A method of welding and sealing the edges of two juxtaposed glass sheets together to seal a vacuum space between the sheets comprises the steps of positioning a radiation absorbant material, such as FeO, VO2, or NiO, between the radiation transmissive glass sheets adjacent the edges and then irradiating the absorbant material, preferably with a laser beam, through at least one of the glass sheets. Heat produced by the absorbed radiation in the absorbant material melts glass in the portions of both glass sheets that are adjacent the absorbant material, and the melted glass from both sheets flows together to create the weld when the melted glass cools and hardens. The absorbant material can be dissolved and diffused into the melted glass to the extent that it no longer absorbs enough energy to keep the glass melted, thus, with appropriate proportioning of absorbant material to source energy power and welding heat needed, the process can be made self-stopping.