The rock acoustic data that provide important information about the formation petrophysics and geomechanics are highly needed to design the wells drilling programs, in addition to, reservoir stimulation and field development plans. The acoustic data acquisition through the conventional methods in the petroleum industry either by logging or lab measurements has many drawbacks as the cost of well log operations and the job time. Determining the acoustic data through the common correlations did not provide high accuracy, and there are limitations for using these correlations. The new trend in the petroleum industry with the fourth industrial revolution is to employ machine learning for such problems to provide effective solutions. Therefore, this study utilized the machine learning for developing prediction models for acoustic compressional and shear slowness using adaptive neuro-fuzzy inference system and support vector machines tools. The study presents novel contributions for predicting acoustic slowness from only the surface drilling data while drilling different formations of composite lithology (limestone, sandstone, shale, and carbonate). The study utilized real field data (2800 data points) to build and test the two models through deep sensitivity analysis, in addition, further testing for the models by another 2800 data points from the same field for the validation phase. The obtained results ensured the capability of machine learning for predicting the acoustic slowness with high accuracy as adaptive neuro-fuzzy inference system (ANFIS) achieved a correlation coefficient (R) higher than 0.98 and error less than 1.43% as average absolute percentage error (AAPE) between the actual and predicted acoustic values. Adaptive neuro-fuzzy inference model showed the highest accuracy during the model training as R was 1.0; in addition, R for testing results showed 0.98, and AAPE ranged from 0.25% to 0.92%. The validation phase ensured the high performance for the acoustic prediction of the developed models as R is higher than 0.98 and AAPE lower than 1.46%. The machine learning applications through the developed models for the acoustic data will provide cost and time savings for acoustic data acquisition for the field applications.