Recent research has focused on assessing the effectiveness of response surface methodology (RSM), a non-machine learning technique, and artificial neural networks (ANN), a machine learning approach, for predicting concrete performance. This research aims to predict and simulate the compressive strength of concrete that replaces cement and fine aggregate with waste materials such as eggshell powder (ESP) and waste glass powder (WGP) for sustainable construction materials. In order to ensure concrete’s durability and structural integrity, a compressive strength evaluation is essential. Precise predictions maximize efficiency and advance sustainability, particularly when dealing with waste materials like ESP and WGP. The response surface methodology (RSM) and artificial neural network (ANN) techniques are used to accomplish this for practical applications in the built environment. A dataset comprising previously published research was used to assess ANN and RSM’s predictive and generalization abilities. To model and improve the model, ANN used seven independent variables, while three variables, cement, waste glass powder, and eggshell powder, improved the RSM. Both the ANN and RSM techniques are effective instruments for predicting compressive strength, according to the statistical results, which include mean squared error (MSE), determination coefficient (R2), and adjusted coefficient (R2 adj). RSM was able to achieve the R2 by 0.8729 and 0.7532 for compressive strength, while the accuracy of the results for ANN was 0.907 and 0.956 for compressive strength. Moreover, the correlation between ANN and RSM models and experimental data is high. The artificial neural network model, however, exhibits superior accuracy.