Annaka Shigeshige served as a bushō during the Sengoku period.  Shigeshige was a retainer of the Yamauchi-Uesugi family and the Kai-Takeda family.  He served as the lord of Annaka Castle in Kōzuke Province.

The Annaka clan were kokujin, or provincial landowners, based in the Usui District of Kōzuke Province.

Shigeshige appears to have been the successor to Annaka Kunai-Shōyū Nagashige.  He was a subordinate of the Yamauchi-Uesugi family who served as the deputy shōgun of the Kantō and a lower-level official of the Nagao clan who were retainers of the Uesugi family.  However, there is a theory that no head of the family before Shigeshige carried the name of Echizen-no-kami, and after his father, Annaka Nagashige and his designated successor, escaped to Echigo Province in service of Uesugi Norimasa, Shigeshige, an illegitimate son, inherited the landholdings and thereafter submitted to the Gohōjō clan.  In 1560, upon the invasion by the Echigo-Uesugi of Kōzuke, Shigeshige affiliated with the Uesugi clan and held possession of Matsuida Castle in the Usui District.

In 1561, following the invasion of Kōzuke by the Takeda, Shigeshige surrendered around the ninth month of 1562 and became a member of a forward-operating unit in Kōzuke.  After submitting to the Takeda, he transferred the role as head of the family to his son, Annaka Kageshige, and retired.  According to one account, Echizen-no-kami was punished for his resistance.  Nevertheless, after surrendering, he did not commit seppuku and was not executed, so the punishment likely occurred in the form of the seizure of Matsuida Castle and orders to retire and enter the priesthood.  Thereafter, his whereabouts are known until 1568.