This article is devoted to the development of technology for improving the efficiency of directional well drilling by predicting and adjusting the system of static and dynamic components of the actual weight on the bit, based on the real-time data interpretation from telemetry sensors of the bottom hole assembly (BHA). Studies of the petrophysical and geomechanical properties of rock samples were carried out. Based on fourth strength theory and the Palmgren–Miner fatigue stress theory, the mathematical model for prediction of effective distribution of mechanical specific energy, using machine learning methods while drilling, was developed. An algorithm was set for evaluation and estimation of effective destruction of rock by comparing petrophysical data in the well section and predicting the shock impulse of the bit. Based on the theory provided, it is assumed that the given shock impulse is an actual representation of an excessive energy, conveyed to BHA. This excessive energy was quantitively determined and expressed as an adjusting coefficient for optimal weight on bit. The developed mathematical and predictive model helps to identify the presence of ineffective rock destruction and adjust drilling regime accordingly. Several well drilling datasets from the North Sea were analyzed. The effectiveness of the developed mathematical model and algorithms was confirmed by testing well drilling data.