The study attempts to estimate the demand for cigarettes in Tanzania and presents simulation results on the effect of the cigarette excise tax on smoking participation, government revenue, and related topics. After briefly summarizing the magnitude and spread of cigarette consumption in the country, the paper reviews some empirical estimates from African and other countries. The 2008 Tanzanian household budget survey was used to estimate the demand for cigarettes in Tanzania. The descriptive statistics suggest that the smoking prevalence for Tanzania is 15.35 percent with low variability across expenditure (income) groups. Smoking intensity and per capita consumption were estimated at 7.08 cigarettes and 1.33 cigarettes, respectively, a relatively low value. A two-part demand equation model was used to estimate various elasticities. For the overall equation, the price elasticities of smoking participation, smoking intensity, and total elasticity were estimated at -0.879, -0.853, and -1.732, respectively. Compared to similar results in other developing countries, the estimates appear quite high. When estimated by expenditure (income) groups, the magnitude of the elasticity appears higher among high expenditure groups than among low expenditure groups. Two simulation exercises were undertaken. First, the effect of different excise rates on smoking participation rate, cigarette consumption, tax revenue, and related responses was estimated and highlighted. Second, the same exercise was undertaken to determine the effect of a given increase in the cigarette excise tax on various expenditure groups. The overall results suggest that an increase in the excise tax on cigarettes in Tanzania would reduce cigarette consumption and increase government tax revenue.