Abstract: The Terahertz (THz) band is between the microwave band and the infrared wave band. It belongs to the category of the far infrared wave and sub-millimeter wave. The terahertz pulsed imaging system delivers the terahertz time domain spectroscopy (THz-TDS), which has a broad wave band property. Such THz-TDS signals not only contain plentiful information but also bring obstacles to the signal analysis and process. Nowadays, the process and analysis of THz-TDS signals are at the beginning stage. Using the geometrical algebra (GA) and based on the physical basis of THz-TDS signals, THz signals were first mapped into vectors in the high dimensional space, and were represented as hyper-numbers. Then, two similarity metrics, the Euclid distance and the similarity function were defined in the language of geometrical algebra, and were used to measure the similarity of the corresponding THz-TDS signals. Detailed computation methods of the metrics were also deduced and presented respectively. And furthermore, those metrics were applied practically in the substance classification and the substance identification based on the THz-TDS signals. Finally, the feasibility and validity of those two similarity measurements are verified by the given experiments. These experiments show that: on condition that signals are obviously distinguished from each other and only a few of the substances are to be identified, all metrics perform well in the substance identification; while on condition that signals are congregated and many substances are to be identified, the similarity function presented performs best.