We present a data-driven algorithm and mathematical model for anomaly alarming at directional drilling. The algorithm is based on machine learning. It compares the real-time drilling telemetry with one corresponding to past accidents and analyses the level of similarity. The model performs a time-series comparison using aggregated statistics and Gradient Boosting classification. It is trained on historical data containing the drilling telemetry of $80$ wells drilled within $19$ oilfields. The model can detect an anomaly and identify its type by comparing the real-time measurements while drilling with the ones from the database of past accidents. Validation tests show that our algorithm identifies half of the anomalies with about $0.53$ false alarms per day on average. The model performance ensures sufficient time and cost savings as it enables partial prevention of the failures and accidents at the well construction.