Accurate detection and localization of mechanical discontinuities are essential for industries dependent on natural, synthetic and composite materials, e.g. construction, aerospace, oil and gas, ceramics, metal, and geothermal industries, to name a few. In this study, a physics-informed machine learning workflow is developed for detecting and locating single, linear mechanical discontinuity in homogeneous 2D material by processing the full-waveforms recorded during multi-point compressional/shear transmission measurements. This work is based on fundamental aspects of simulation of wave propagation, signal processing, feature engineering, and data-driven model evaluation. k-Wave simulator is implemented to model the compressional and shear wave transmission through the 2D numerical model of a material containing single mechanical discontinuity. For a specific source-sensor configuration, the newly developed data-driven workflow can detect and locate the mechanical discontinuity with an accuracy higher than 0.9 in terms of coefficient of determination. AdaBoost regressor with k-Nearest Neighbor as a base estimator significantly outperforms all other models. In terms of sensitivity to noise, k-Nearest Neighbor is the most robust to both gaussian and uniform distributed noise.