The distortion of a two-dimensional fuel strip that arises due to interaction with a vortex pair structure is examined analytically, with emphasis placed on the evolving flame structure and the consumption of reactants due to straining of the flame. Two different theoretical situations are considered: one in which the diffusion flames bounding an infinitely long fuel strip interact with a counter-rotating vortex pair, and another in which the corners of the flame bounding a semi-infinite fuel strip coincide with the vortex pair. The second case is particularly relevant as a 2D analog of the vortical flame structure formed at a circular orifice or nozzle.