The future existence and development of potential water resources hinge mainly on thernpast features of hydrological behaviors. Unfortunately, these features are not availablerndepending on the socio-economic and political stability of the country. Streamflowrnmeasurement is one of the features of our country Ethiopia and other developed andrndeveloping countries suffer to estimate. This study aims to identify the rainfall-runoffrnrelationships and develop an empirical equation that can be used to estimate the meanrnannual flow for ungauged catchments in the Abbay river basin. rnBased on the influence on runoff generation and easy availability climate variable (rainfall)rnand physiographic variables (catchment area, land slope, and elevation) are selected as arnpredictor of flow in the Abbay river basin. The selected 27 hydrometric stations split intorntraining (70%) and test (30%) datasets for the periods 1981 to 2013. Linear and non-linearrnforms of the equation were tested to relate annual flow and annual rainfall at eachrnhydrometric station. A regression model used to relate the dependent variable mean annualrnflow and independent variables climate and physiographic characteristics. Statistical testsrnused for selecting the best trustworthy equation. rnAnalysis of the relationship between runoff and rainfall demonstrates fully dominance ofrnnon-linear forms of equations and development of an empirical equation shows that therncatchment area, mean annual rainfall, and the average elevation is the trustworthy modelrnwith both Rrn and Ns value of 0.96. Furthermore, the validation analysis strengthens thisrnequation statistically and graphically. The result reveals that relationships of rainfall andrnrunoff are non-linear and the size of the catchment, rainfall, and elevation of the catchmentrnhighly governs the amount of flow expected at the outlet. On this root, it is recommendedrnthat interested professionals on the estimation of flow at ungauged catchments carefullyrndelineate the area, estimate rainfall with enough rain gauge stations, and consider elevationrnas the factor. Moreover, further studies need to incorporate additional catchmentrncharacteristics to identify other influential factors in the formation of runoff. rn2