Flue cured tobacco has been an important crop for the Zimbabwean economy historically in terms of foreign currency earnings and employment creation. Between 1980 and 2000, there is a general increase in tobacco output, followed by a sharp decline from 2001 up to 2008 and then output starts to increase again. Flue cured tobacco output as measured by the quantity that is delivered to the auction floors is used to estimate supply elasticity. The objective is to determine if flue-cured tobacco supply is price elastic and whether price incentives alone will boost supply in the short -run. Time series data on flue cured tobacco output, prices, production costs, prices of major competing crops, the exchange rates and inflation are analysed to model the price elasticity of flue cured tobacco between 1980 and 2010. The Augmented Dickey –Fuller unit root test is performed to test the variables for stationarity. The data generating processes show these data series to be non-stationary and therefore OLS estimations would be biased. The data series are differenced and the Engel-Granger procedure is performed to test for cointegration. The Error Correction Model approach is used to estimate flue cured tobacco supply. Flue cured tobacco supply is found to be price inelastic in the short –run.