Physically based mathematical models were developed by use of generalized-least-squares regression analyses to estimate long-term 95-, 98-, and 99-percent duration discharges for ungaged streams in Massachusetts. Duration discharges for 61 sites were used in the recession analyses; 37 sites were streamflow-gaging stations and 24 sites were low-flow partial-record stations. The duration discharges were related to basin chacteristics measured from digital data bases, by use of geographic information systems computer software. Significant chacterisfics used in the models were drainage area, area underlain by stratified-drift deposits per unit of stream length in the basin, and a surrogate for the effective head on the aquifer in the stratified-drift deposits, computed by subtracting the minimum basin elevation from the mean basin elevation. Standard errors of prediction were 57.5, 85.6, and 98.5 percent for models for the 95-, 98-, and 99-percent duration discharges, respectively. Model error variances were about 10 times the sampling error variances, indicating that the precision of future models are likely to be improved more by obtaining better measurements of basin characteristics or by adding new sites to the analyses than by collecting more streamflow data at the sites presently used in the analyses. The models were used to predict duration discharges for 35 selected sites in the Concord River, Noah Coastal, South Coastal, Narragansett and Tenmile River Basins. Ninety-perrcent prediction intervals were computed for the estimates at each of the sites, except at sites where values of the independent variables were outside the ranges of those for the sites used in the regression analyses.