Since 2018, a scientific research project, the “Lilybaeum Project”, is being carried out by a collaboration of physicists and archaeologists. The goal is to apply forefront analysis techniques to the investigation of archaeological artefacts, both in situ and in the laboratory. The first case study presented in this paper concerns the original investigation through X-ray computed tomography of a collection of objects from the Regional Archaeological Museum of Lilybaeum, in Marsala, Italy. In addition to a very significant collection of clay jars mostly from children's graves of the ancient Lilybaeum necropolis, an unprecedented analysis of wooden planks belonging to the only existing wreck of a Punic Ship kept in the Museum is presented.