This paper derives analytical solutions of fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium. This investigation extends the work of Cheng (2006) to a situation where Soret effect is present and the flow is both aided and opposed. The influence of the controlling parameters on the flow characteristics has been seen to be higher for double diffusion in the absence of Soret effect than in the presence of Soret effect. It is found that the presence of Soret effect reduces the dependence of the volume flow rate, the total heat rate and the total species rate on the inner radius-gap ratio and on the modified Darcy number.