This paper is a theoretical study of a radial standing wave, which can be applied in the so-called traveling wave reactor (TWR). Two-dimensional cylindrical core geometry is considered and the fuel is assumed to drift radially, which corresponds to a radial fuel shuffling scheme in practice. A one-group diffusion equation coupled with burn-up equations is set up, where the burn-up solution is obtained numerically. The uranium-plutonium (U-Pu) conversion cycle with pure 238U as fresh fuel is considered under conditions of a typical sodium cooled fast reactor with metallic uranium fuel loaded. The asymptotic problem is solved by a time-stepping iteration scheme and the radial standing wave solution is obtained together with certain eigenvalue keff.The neutron flux, the neutron fluence and the net neutron generation cross section are presented and discussed for the inward fuel drifting motion.