The development of human society over the past century has led to an explosion in population numbers and a migration of settlements to river valleys, which have become increasingly exposed to the risk of flooding. In this context, the scientific community has begun to work on identifying mathematical and spatial models that can help to identify areas at risk as quickly as possible. The present article is one that follows this objective, proposing an automatic model that can be implemented in ArcGIS and that aims to identify only areas at risk of flooding using a single file, the DEM. The novelty of this article and the usefulness of the method are given precisely by the fact that it is possible to quickly find out which areas may be exposed to flooding, i.e., water accumulations, only based on relief, which is extremely useful for local authorities. The analysis was conducted on all hierarchy orders, according to the Horton–Strahler classification system, for the entire Romanian territory. The results consist of a polygonal vector layer in shapefile format, containing an attribute table with all the initial, intermediary, and final calculations in separate numeric fields. Each parameter was normalized in order to obtain the final morphometric flood vulnerability score. Postprocessing these results involved applying a Principal Component Analysis to identify weights for the components that encompass all morphometric parameters. Each drainage basin reveals a dimensionless morphometric flood vulnerability score value that is comparable with all other basins in Romania.