In Greek mythology, the name Alcimache may refer to:Alcimache, daughter of Aeacus and the mother of Medon by Oileus. Alternately, Alcimache was a daughter of Phylacus and mother of Ajax the Lesser, and on that account was equated with Eriopis by the author of Naupactica. Alcimache or Alcimacheia, daughter of Harpalion, a Maenadic follower of Dionysus; she participated in the god's Indian campaign and was killed by Morrheus (Μορρεὺς). Alcimache, a surname of Athena.