Pump systems are often critical in industrial environments, and unexpected failures can lead to significant downtime. This work proposes a method that uses long short-term memory (LSTM) networks to detect and classify anomalies in pump sensors. The approach leverages temperature and vibration signals to identify overheating, increased vibration, combined anomalies in both signals, and short-lived transient spikes. Synthetic data helps illustrate the various operating states, while the LSTM architecture is designed to capture temporal dependencies in the sensor data. The experimental results suggest that LSTM-based solutions can provide early warnings of anomalies and enable better maintenance strategies for real-world pump applications.