Abstract: To characterize the internal gas flow of unburnt cigarettes with different cigarette material designs, a nonlinear model and numerical solver are developed based on the Darcy-Forchheimer law and cigarette material design elements. A series of flow experiments and numerical calculations are conducted under different puffing flow rates and modes for non-filter-ventilated and filter-ventilated cigarettes, as well as slim and regular cigarettes. Meanwhile, the influence of the nonlinear effect on draw resistance is quantitatively analyzed for cigarette internal flow under different ventilation conditions. The results indicate that: 1) The model and solver capture the nonlinear relationship between flow rate and draw resistance across cigarettes, and can accurately predict the pressure and flow rate distribution in cigarettes. 2) For internal flow calculations in unburnt cigarettes under a wide range of operating conditions, the nonlinear model is more accurate than the linear model and linear regression, and the average relative error of the nonlinear model in predicting draw resistance is less than 3%, with R² > 0.99. 3) The nonlinear resistance is more significant in the tobacco rod than in the filter section, and filter ventilation can reduce both the local contribution and the cumulative increment of the nonlinear effect on draw resistance. The proposed model and solver provide methodological references for analyzing cigarette internal flow and developing cigarette products.