Flood hazard mapping and the design of many water infrastructures are commonly based on the use of a single hydrologic variable, the design instantaneous peak flow. However, the entire flood hydrograph (or at least the flood volume) is needed in many circumstances, including the evaluation of potential risks in dam safety analysis, the design of detention basins, the application of inundation methods or of river levee failure. While many efforts have been made in the last decades to improve the peak flow estimation in a generic section of a river network, procedures for the systematic estimation of flood volumes in ungauged sections over large regions are not consolidated yet. In this paper, the estimation of the flood volumes in ungauged basins is developed, based on the Flood Reduction Function (FRF), a parsimonious representation of the flood hydrograph structure. The FRF is a volume-duration relationship that allows to easily extract flood hydrographs based on few parameters, that exhibit marked regularity. Based on data from 87 basins (763 station-years of flood hydrographs) in the Northwest Italy, a two-parameter FRF has been considered to build a regionalized estimation procedure. The estimation of FRF parameters in ungauged basins has been obtained with different procedures. Results suggest that the multiple linear regression model can be an effective method to estimate the FRF in ungauged basins, producing nearly unbiased predictions and design hydrographs which reasonably resemble the observed ones.