Of course, we cannot really speak of a "literature" of the Shang period, a time when just a kind of script was invented. The oldest documents of the Chinese script date from the reign of King Wu Ding (Wuding) 武丁 (around 1150 BC) and are actually archival materials incised on oracle bones stored in the royal archives.
A second type of writings which are likewise rather documents than literature are the scarce inscriptions on ritual bronze vessels.
Another type of literature of the Shang period are the speeches of the Shang rulers to be found in the Shangshu 尚書, also called Shujing 書經, the "Book of Documents". These speeches, contained in the part Shangshu 商書 "The Book of Shang" are written in a very ancient language, but it can be assumed that they are not really documents from the Shang period but were compiled at the later date, during the Western Zhou period or even later. The archaic language style was in this case imitated artificially.
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