The purpose of this paper is to report quantitative data and models for the flow stress for the computer simulation of friction stir welding (FSW). In this paper, the flow stresses of the commercial 6061 aluminum alloy at the typical temperatures in FSW are investigated quantitatively by using hot compression tests. The typical temperatures during FSW are determined by reviewing the literature data. The measured data of flow stress, strain rate and temperature during hot compression tests are fitted to a Sellars–Tegart equation. An artificial neural network is trained to implement an accurate model for predicting the flow stress as a function of temperature and strain rate. Two models, i.e., the Sellars–Tegart equation and artificial neural network, for predicting the flow stress are compared. It is found that the root-mean-squared error (RMSE) between the measured and the predicted values are found to be 3.43 MPa for the model based on the Sellars–Tegart equation and 1.68 MPa for the model based on an artificial neural network. It is indicated that the artificial neural network has better flexibility than the Sellars–Tegart equation in predicting the flow stress at typical temperatures during FSW.