In the present paper we propose a new model of monthly river flow rate as a simple nonlinear function of air temperature and rainfall. Response surface methodology is used to analyze the observed monthly flow rates from 1950 to 1990 for Great Morava River, as the largest domestic river in Serbia. Obtained results indicate significant linear and quadratic effect of both individual factors, while two-factor interactions show significantly smaller influence, indicating occurrence of maximum flow rate for low temperature and high rainfall regime. Statistical reliability of the proposed model is verified by internal and external validation, the latter of which included comparison of predicted and observed values from 1991 to 2012. It is shown that predicted flow rates exhibit a similar statistical pattern as observed ones, with a satisfying value of Nash–Sutcliffe coefficient (NSE = 0.73), although the derived model cannot capture well the highest flow rates. Obtained results further indicate the sequence of residuals represents random time series, which is confirmed by appropriate test statistics and surrogate data testing. The advantage of using the derived model for hydrological simulations in river basins instead of existing ones lies in its explicit mathematical form, making it suitable for quick and reliable estimation and prediction of monthly flow rates.