A non-intrusive inspection system, including apparatuses and methods, for non-intrusively inspecting containers such as, without limitation, those employed to transport items in international commerce. The non-intrusive inspection system is configured to generate and scan a container with multiple bremsstrahlung, or x-ray, beams having multiple spectra and directed at the container in multiple directions and planes separated by one or more angle(s). Using data collected from such scanning, software of the non-intrusive inspection system generates three-dimensional images of the items present in a container, calculates the volumes and densities of such items, computes effective "Z" numbers, and distinguishes between multiple materials, or elements, of such items. By employing multiple bremsstrahlung beams directed upon a container in multiple planes, the non-intrusive inspection system reduces the number of orientations and geometries of items within a container that might otherwise be employed to avoid the detection of harmful materials being transported within a container.