Before the end of World War I, Syria had no museums. The museum of Damascus was established in 1919, one year before the establishment of the French mandate, and is thus oldest cultural heritage institution in Syria. It was first located in al-Madrasa al-Adiliyeh, an historical building in the old city dating to the 12th/13th centuries. A new building was constructed between 1936 and 1979, and it became what is today the National Museum of Syria. Since these years, the collections have been enriched by many new finds from numerous excavations. The objects are divided chronologically: prehistory, ancient Orient, Greek, Roman Byzantine, Islamic antiquities, and modern art.

The museum curates some 5,000 cuneiform tablets. These tablets are from:

• Tell Al-Hariri (Mari): approximately 3,000 cuneiform tablets and fragments (school tablets, literary and administrative texts, contracts) have been excavated since 1998 in a private house at the north east of the royal palace. They are to be dated to the Old Babylonian period. The texts are being studied by A. Cavigneaux form the University of Geneva and will be published soon. The museum curates also some Mari tablets from the former excavations (before 1998).
• Tell Mardikh (Ebla): only 4 tablets (dating from the Early Dynastic III period).
• Ras Shamra (Ugarit): roughly 1,500 tablets from the Middle Babylonian period, of which 600 texts were recently found in the house of Urtenu and are mostly written in Akkadian language.
• Ras Ib Hani: 130 tablets from the Middle Babylonian time, comparable to the Ras Shamra ones.
• Tell Sabi Abyad: only one tablet that dates to the Middle Assyrian period.
• Tell Taban (Tabatum), at 20 km south of Al-Hassake. Roughly 500 tablets, mainly from the Middle Assyrian period, have been unearthed there by a Japanese team from the Institute for Cultural Studies of Ancient Iraq of Kokushikan University.