The area encompassing the Eastern branch of the East African Rift System (EARS: Afar-Ethiopia-Turkana) and associated plateaux is an ideal region to investigate extension and magmatism associated with rupturing continental lithosphere. Ethiopia covers an important part of the EARS. It contains the major section of the ca. 5000 km Afro-Arabian rift and includes the transition between the Arabo-Nubian-Shield and the Mozambique Belt. A compilation of over 45000 onshore and offshore gravity stations covering the EARS and adjacent regions (Eastern Sudan, Red Sea and Gulf of Aden margins) has been made and forms the major data set upon which this study is based. The database is re-evaluated and re- processed using consistent procedures and has an estimated Bouguer gravity error of 1.5-4.5 x10-5m/s2. An attempt has been made to fill data gaps by merging the terrestrial data with GRACE satellite data. A regional 3D density model is developed using the GIS functionalities of a potential field-modelling program (IGMAS) and integrates seismic constraints with information from isostatic models, global seismic tomography, geological, geochemical, petrological and experimental results. Thirty parallel east-west sections through the EARS are modelled to a depth of 150 km. The 3D density structure reproduces the Bouguer gravity anomaly with a high accuracy (standard deviation of 16x10-5 m/s2). Misfits are attributed to errors in the gravity database and unconsidered structures. Analysis of the new gravity database and 3D modelling offers new information on the EARS, namely the isostatic state of the region, crust and upper mantle structures, basement and optimised Moho maps, quantification of modelled units and estimation of rigidity, among others. Based on the present data and new additional data sets, short and long-term scientific goals can be identified. Some of the most important are: further rigidity calculations using the 3D density model, joint modelling of gravity and magnetic data in selected areas, updating of the gravity network in Ethiopia, heat flow measurements in the Main Ethiopian rift and adjacent plateau, and integrated geoscientific experiments in the broadly-rifted region of southern Ethiopia