An Echo State Network (ESN) can make multi-step predictions since it can process temporal information without the training difficulties encountered by conventional recurrent neural networks. An ESN is applied in this paper to make multistep predictions of solar irradiance, 30 minutes to 270 minutes into the future. The ESN is trained and tested using two performance metrics (correlation coefficient and mean squared error) on meteorological and solar data recorded at the National Renewable Energy Laboratory Solar Radiation Research Laboratory in Golden, Colorado. When feedback of target outputs is utilized, an improvement is seen for the first performance metric, while no significant change is seen for the second performance metric. Additionally, accuracy is observed to diminish significantly as the time horizon for the predictions increases.