It is important in geophysical applications to relate the compressional and shear ultrasonic wave velocities of micritic limestone to its porosity, volume fraction and density of micrite grains as well as the effective confining pressure. In this paper, this difficulty task is successfully realized by using the most relevant machine learning methods: The artificial neural network method, the support vector machine method and the extreme gradient boosting method (XGB). A relevant dataset available in literature is considered to train and test the models. It is observed that the XGB method significantly outperform the other methods in term of accuracy and training time. It allow obtaining a very high R-squared value of 0.96 and a very small relative root mean squared error of 3% while predicting the sonic velocities from other petrophysical properties. The robustness of the models is also confirmed by studying the sensitivity of the random splittings between the training and the testing sets (C) 2020 Elsevier B.V. All rights reserved.