Kunkut of Cheju Island and its myths are fairly old cultural assets. This study has been done to find out the characteristics and meanings in family structure in myths. There are myths in Kunkut of Cheju Island such as : Bepodoupchim, Sengbulhalmang-bonpuli, Chokong-bonpuli, Ikong-bonpuli, Samkong-bonpuli, kanglim-bonpuli, Mengkam-bonpuli, Sekyoung-bonpuli, Chilsung-bonpuli, Munjun-bonpuli, etc. As for the characteristics in the family structure, the attention to the children is centered to twins, only daughter and youngest one. Throughout generations, heaven-father and earth-mother, old man and wife praying for having a son, women sufferings due to giving birth and upbringing, looking for fathers by sons born without them, troubles between wife and lover or between step mother and former wife\'s son, marriage between human being and animal, respect to old skull. The myths were abundant in the ancient times but there is no way to be brought those myths back to life. As an example, the centered attention to the youngest child plays a key role in pursuit of those myths of ancient times. The story of Gurungdungdungsinsunbi, which is about snake and, at the same time, Jang Ja family\'s youngest daughter has most important role, has something in common with myths in Kunkut of Cheju Island. Therefore, this story could have been one of those lost myths of ancient times. From this point of view, the fact that Hwanwoong was the illegitimate son of Hwan-In in Dankun myth could be related to the social tendency of the ancient times in which more importance was given to the youngest child than to the first one.