Experimental design and response surface modeling techniques generate a regression model approximation of the outcome of complex basin models. Uncertainty is determined by Monte Carlo sampling of the response surface, instead of the basin model itself, which would be considerably more expensive. Additional advantages are that interaction effects are taken into account; that parameters are ranked according to their influence on the response, suggesting those that may be discarded if they are not important; and that the response surface can be constrained to data, thereby defining the valid parameter space and reducing the uncertainty of the outcome variable. As an example application, the uncertainty of petroleum generation and expulsion from source rocks in the Gippsland Basin, southeast Australia, is calculated using 1-D thermal and maturity modeling. Main parameters are heat-flow history and thermal-conductivity contrast. A linear screening design shows that heat-flow history has the main effect on petroleum quantities expelled, and calibration to available temperature data allows us to fix present-day heat flow. The resulting second-order response surface is based on heat flow during rifting and coal content. Petroleum expelled from the total sediment column is between 70 and 115 kg/m². This result was obtained with 26 model experiments.