The Planar Flow Melt Spinning Process for the Rapid Solidification of metallic materials is analyzed using a mathematical model based on the principles of capillary fluid dynamics and solidification heat transfer. The results suggest the existence of a region of slowly recirculating flow inside the melt puddle which acts as a lubricant between the nozzle and the wheel. Markedly different thermal conditions across the ribbon thickness are also predicted by the model, as are the resultant microstructural variations across such thickness. The results of the model compare well with the available experimental evidence. The model is sufficiently general as to be immediately applicable to the study of other meniscus controlled continuous casting processes.