The results of experimental and theoretical studies of streamline deflection in diffusion flames are presented for approximately streamwise flames stabilised on a Parker-Wolf hard burner. It is shown that both the displacement of the dividing streamline from the flame sheet and the phenomenon of streamline refraction through the flame sheet can be predicted at least qualitatively by a simple linearised model for the diffusion flame in Oseen flow, in which only the irrotational pressure, temperature and composition waves are considered. Although this treatment involves the description of flame properties in terms of disturbances from freestream values, essentially the same results are obtained by linearisation about flame sheet properties. The question is left open whether the present mechanism for streamline refraction is that which leads to transfer of fuel or oxidant across the base of the flame close to extinction, eventually leading to flame lift and complete extinction.