Elias I (also Hélie or Élie) (died 11 July 1110), called de la Flèche or de Baugency, was the Count of Maine from 1093. He was the son of the lord of La Flèche, John de Beaugency, and his wife Paula, daughter of Herbert I, Count of Maine.
In 1093, 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.
Elias married Matilda, daughter of Gervais, Lord of Château-du-Loir. Their daughter, Eremburg, married Fulk V of Anjou. In 1109, says Orderic Vitalis, Elias remarried to Agnes, the daughter of 'William of Poitou' and relict of Alfonso VI of Castile. This is perhaps confused, as the name and parentage match that of Alfonso's first wife, but she last appears thirty years earlier. It has been suggested that the true bride was Alfonso's widow Beatrice.