The time dependent interaction of a laminar diffusion flame with a single plane vortexand with a stretched line vortex is examined with the aim of determining the flame configuration and the augmentation to the reactant consumption rate resulting from the interaction. Elements of the resulting curved flame sheets behave essentially as isolated flamesuntil the neighboring flame sheets become so closely spaced that they interact and consumethe intervening reactant. This process creates a core of combustion products with external isolated flame surfaces. The augmentation of the reactant consumption rate results bothfrom the local straining of the flame in its own plane and from the overall increase in flame surface area. Three examples are treated in detail. The first is the plane problem in which an initially straight flame is distorted by a vortex. In the second, the situation is similar except that the problem is expanded to three dimensions and the vortex line is being stretched along its own axis. Finally, the effects of the density change resulting from the heat release are examined.