A surviving relative told US media that the boat's captain had told the 31 passengers not to put on life jackets.
The amphibious "duck boat" capsized during a rapidly deteriorating thunderstorm on Table Rock Lake, a popular tourist attraction.
Missouri Highway Patrol said the ages of the deceased range from one to 70.
The woman who says she lost nine members of her family has been named as Tia Coleman. She is one of two in her family to have survived.
