Johnson County Sheriff Charles Heiss said the teen and two others were in a flat-bottom jon boat at about 6 p.m. Sunday when they hit a tree and began taking on water.
The two other boys, age 17, were able to make it to land safely, but there was no sight of the third.
Heiss said heavy weekend rains have caused the creek to become unusually high and fast-moving, making for a dangerous situation not only for boaters, but for searchers.
Johnson County Fire Protection District 2 Chief David Miller said Van Meter is presumed dead because of the amount of time he has been missing. Dozens of searchers are trying to recover Van Meter's body, walking through the creek in quarter-mile sections.
Friends, family members and classmates have been gathering at the search command post, waiting for news and offering their help.
They describe Van Meter as an outgoing, laid back farm boy who loved to be outdoors. Family members said he just graduated from a class of 16 at Kingsville High School and planned to farm with his family.
A Johnson County dive team is being joined by several other local and state agencies in the search for the teenager. Miller said searchers will be looking for Van Meter's body until the sun goes down.
Flooded Missouri waterways are to blame for at least two other deaths, officials report.
A teenager's body was recovered near Eldon on Saturday after being swept away in fast-rising water. On Friday, a 72-year-old man drowned in flash flooding in Lawrence County.
And authorities were still trying to determine if the drowning of a 55-year-old man in a pond in Ellington was flood- or weather-related.