•Optimization of the use of industrial waste of different natures in cementitious mortars.•Artificial neural network together with response surface for dynamic characterization of cementitious mortars.•Natural frequency increase in mortars with polyurethane waste.•Foundry sand with polyurethane are able to increase the damping of cementitious mortars. Although many studies have reported on the application of experimental, statistical, numerical, and computational tools to composite structures, few have focused on the use of analysis of variance (ANOVA) to analyze experimental data and Artificial Neural Network (ANN) as a technique to predict the modal responses of Portland cement mortars. In this study, by means of DOE and ANN the modal responses of portland cement mortars with polyurethane waste and foundation sand from exhaustion were investigated. The tests were performed by means of free vibration and the analyzed responses were natural frequency and damping factor. The experimental results indicated that the combined PU and FES waste can significantly change the natural frequency and damping of the mortars. This change, when compared to the reference samples, can reach an increase of 11.6% or decrease of 21.7%, depending on the percentage of waste used. The ANN trained with the experimental data showed a high correlation to predict the experimental results.