This study presents a data-driven approach using machine learning algorithms to provide predicted analogues in the absence of acoustic logs, especially while drilling. Acoustic logs are commonly used to derive rock mechanical properties; however, these data are not always available. Well logging data (wireline/logging while drilling - LWD), such as gamma ray, density, neutron porosity, and resistivity, are used as input parameters to develop the data-driven rock mechanical models. In addition to the logging data, real-time drilling data (i.e., weight-on-bit, rotation speed, torque, rate of penetration, flowrate, and standpipe pressure) are used to derive the model. In the data preprocessing stage, we labeled drilling and well logging data based on formation tops in the drilling plan and performed data cleansing to remove outliers. A set of field data from different wells across the same formation is used to build and train the predictive models. We computed feature importance to rank the data based on the relevance to predict acoustic logs and applied feature selection techniques to remove redundant features that may unnecessarily require a more complex model. An additional feature, mechanical specific energy, is also generated from drilling real-time data to improve the prediction accuracy. A number of scenarios showing a comparison of different predictive models were studied, and the results demonstrated that adding drilling data and/or feature engineering into the model could improve the accuracy of the models.