The effects of proximate, ultimate and elemental analysis for a wide range of American coal samples on Free-swelling Index (FSI) have been investigated by multivariable regression and artificial neural network methods (ANN). The stepwise least square mathematical method shows that variables of ultimate analysis are better predictors than those from proximate analysis. The non linear multivariable regression, correlation coefficients (R²) from ultimate analysis inputs was 0.71, and for proximate analysis input variables was 0.49. With the same input sets, feed-forward artificial neural network (FANN) procedures improved accuracy of predicted FSI with R² = 0.89, and 0.94 for proximate and ultimate analyses, respectively. The ANN based prediction method, as a first report, shows FSI is a predictable variable, and ANN can be further employed as a reliable and accurate method in the free-swelling index prediction.