Élie (also Hélie or Elias), called de la Flèche or de Baugency, was the Count of Maine, succeeding his cousin Hugh V, Count of Maine.
He was the son of Jean de la Flèche and Paula, daughter of Herbert I, Count of Maine.
In 1092, his cousin Hugh V sold Maine to him for 10,000 shillings. With the support of Fulk IV of Anjou, he continued the war with Robert II of Normandy. After Robert's departure with the First Crusade, Elias made peace with William Rufus, Robert's regent in Normandy.
In 1090 Elias married Matilda, daughter of Gervais II, Lord of Château-du-Loir. They had a daughter:
Eremburg, married Fulk V d'Anjou.
In 1109, Élie remarried to Agnes, the daughter of William de Poitou and relict of Alfonso VI de Castile. She died the following year.
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