Selective ring-opening polymerization of a 1,4-anhydro-2-O-(tert-butyldimetbylsilyl-3-deoxy-alpha-D-ribopyranose (A3DSR) was carried out by a number of Lewis acid catalysts to give stereoregular 3-deoxyribofuranans. It was found that the polymerization by phosphorus pentafluoride catalyst at -78 degrees C gave a poly(A3DSR) with [alpha](D) = +85 degrees consisting of 1,5-alpha-linked furanosidic units in the polymer backbone, while the polymerization at 0 degrees C gave a poly(A3DSR) with [alpha](D) = -46 degrees which was composed of 1,5-beta-linked furanosidic units. 1,4-Anhydro-3-O-(tert-butyldimethylsilyl)-2-deoxy-alpha-D-ribopyranose (A2DSR) was also polymerized by Lewis acid catalysts to give stereoirregular polymers consisting of mixed structures of alpha- and beta-units. The desilylation of the poly(A3DSR) was carried out by a fluoride ion in THF to give a 3-deoxy-(1-->5)-alpha-D-ribofuranan. The structure analysis of polymers was performed by C-13 NMR spectroscopy, specific rotation, and hydrolysis studies. The effects of catalyst, polymerization temperature, and time on the polymer stereoregularity were examined, and the mechanism of the stereoregular polymerization was discussed.