We propose an Automatic Threat Detection (ATD) algorithm for Explosive Detection System (EDS) using our multistage Segmentation Carving (SC) followed by Support Vector Machine (SVM) classifier. The multi-stage Segmentation and Carving (SC) step extracts all suspect 3-D objects. The feature vector is then constructed for all extracted objects and the feature vector is classified by the Support Vector Machine (SVM) previously learned using a set of ground truth threat and benign objects. The learned SVM classifier has shown to be effective in classification of different types of threat materials. The proposed ATD algorithm robustly deals with CT data that are prone to artifacts due to scatter, beam hardening as well as other systematic idiosyncrasies of the CT data. Furthermore, the proposed ATD algorithm is amenable for including newly emerging threat materials as well as for accommodating data from newly developing sensor technologies. Efficacy of the proposed ATD algorithm with the SVM classifier is demonstrated by the Receiver Operating Characteristics (ROC) curve that relates Probability of Detection (PD) as a function of Probability of False Alarm (PFA). The tests performed using CT data of passenger bags shows excellent performance characteristics.