The Stochastic Streamflow Models (SSMS) are time series models for precise prediction of hydrological data useful in hydrologic risk management. Nowadays, deep learning networks get many considerations in time series forecasting. However, despite their theoretical benefits, they fail due to their drawbacks, such as complex architectures, slow convergence and the vanishing gradient problem. In order to alleviate these drawbacks, we propose a new stochastic model applied in problems that involve stochastic behavior and periodic characteristics. The new model has two components, the first one, a type of recurrent neural network embedding the echo-state (ESN) learning mechanism instead of conventional backpropagation. The last component adds the uncertainty associated with stationary processes. This model is called Stochastic Streamflow Model ESN (SSMESN). It was calibrated with time series of monthly discharge data from MOPEX data set. Preliminar results show that the SSMESN can achieve a significant prediction performance, learning speed. This model, can be considered a first attempt that applies the echo state network methodology to stochastic process.