Due to the relatively high activity concentrations of (210)Po and (210)Pb that are found in tobacco and its products, cigarette smoking highly increases the internal intake of both radionuclides and their concentrations in the lung tissues. That might contribute significantly to an increase in the internal radiation dose and in the number of instances of lung cancer observed among smokers. Samples of most frequently smoked fine and popular brands of cigarettes were collected from those available on the Egyptian market. (210)Po activity concentrations were measured by alpha spectrometry, using surface barrier detectors, following the radiochemical separation of polonium. Samples of fresh tobacco, wrapping paper, fresh filters, ash and post-smoking filters were spiked with (208)Po for chemical recovery calculation. The samples were dissolved using mineral acids (HNO(3), HCl and HF). Polonium was spontaneously plated-out on stainless steel disks from diluted HCl solution. The (210)Po activity concentration in smoke was estimated on the basis of its activity in fresh tobacco and wrapping paper, fresh filter, ash and post-smoking filters. The percentages of (210)Po activity concentrations that were recovered from the cigarette tobacco to ash, post-smoking filters, and smokes were assessed. The results of this work indicate that the average (range) activity concentration of (210)Po in cigarette tobacco was 16.6 (9.7-22.5) mBq/cigarette. The average percentages of (210)Po content in fresh tobacco plus wrapping paper that were recovered by post-smoking filters, ash and smoke were 4.6, 20.7 and 74.7, respectively. Cigarette smokers, who are smoking one pack (20 cigarettes) per day, are inhaling on average 123 mBq/d of (210)Po and (210)Pb each. The annual effective doses were calculated on the basis of (210)Po and (210)Pb intake with the cigarette smoke. The mean values of the annual effective dose for smokers (one pack per day) were estimated to be 193 and 251 microSv from (210)Po and (210)Pb, respectively.