The focus of this study is to forecast the 28-day compressive strength and split tensile strength of concrete with various percentages of jute and coconut fibres mixed with quarry dust. The response surface methodology (RSM) and the artificial neural networks (ANN) methods were adopted for 3 variable process modelling (coconut fibres of 0% to 2.5%, jute fibres of 0% to 2.5%, and quarry dust of 0% to 25% by weight of cement). The RSM Box−Behnken design (BBD) method was adopted to design the experiments. Test results showed that compressive strength of 34.6 N/mm2 was obtained for concrete with 0% jute, 0% coir, and 12.5% quarry dust. Similarly, the maximum split tensile strength of 3.8 N/mm2 was obtained for concrete with 1.25% jute fibres, 1.25% coconut fibres, and 12.5% quarry dust. ANOVA and Pareto charts were used to assess regression models for response data. Each progression variable’s statistical significance was assessed, and the resulting models were expressed as second-order polynomial equations. Levenberg−Marquardt (LM) algorithm with feed-forward back propagation neural network was used for assessing the compressive strength and split tensile strength of concrete. The statistical data, root mean square error (RMSE), mean absolute error (MAE), mean absolute and percentage error (MAPE), and determination coefficient (R2) show that both techniques, ANN and RSM, are effective tools for predicting compressive strength and split tensile strength. Furthermore, RSM and ANN models have a high correlation with experimental data. However, the response surface methodology model is more accurate.