People lived in the environs of Avilčiai since ancient times as evidenced by archeological artifacts. During the Soviet times the village had a school and a library. There were 21 families (95 people) living there more than 60 years ago. After the melioration, most of the people moved out because their houses were torn down. There is almost no youth in Avilčiai so the school was closed down.
A ritual stone with a hole that looks like a man's foot is located near the village.