Two hybrid back-propagation neural network (BPNN) models optimized by two heuristic search algorithms, namely genetic algorithm (GA-BP) and particle swarm optimization (PSO-BP), are proposed in this paper to predict radial maximum wall shear stress instead of traditional computational fluid dynamics (CFD) methods. The two proposed models are trained and validated using a database of 150 radial maximum wall-shear-stress values obtained via CFD simulations. The best fit model is identified from various BPNN models based on the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), balancing the trade-off between goodness-of-fit and model complexity. The model performance is evaluated by MAE, RMSE, regression coefficient (R), and Nash-Sutcliffe efficiency (NSE). The best fit model is a three-layered BPNN model consisting of a 4:4:1 topology. In almost all evaluation indicators, the two hybrid BPNN methods outperform three existing algorithms, namely classical BPNN, random forest (RF), and gradient boosting decision tree (GBDT). Both PSO-BP and GA-BP can provide a more precise assessment of radial maximum wall shear stress, with maximum errors being 5.81% and 8.24% respectively. The proposed PSO-BP prediction model is promising and has great feasibility in predicting the radial maximum wall shear stress of UHP water-jet nozzle in engineering applications.