The film, which echoes Mark Twain and his novel "The Adventures of Huckleberry Finn", centers on Ellis - played by up-and-coming actor Tye Sheridan, who was 14 at the time.
Along with best friend Neckbone, he comes across the mysterious Mud (McConaughey) who is living alone on an island.
The boys discover he is on the run for a serious crime, but has come back to the area to find the love of his life Juniper, played by Witherspoon, whom he dreams of whisking away to Mexico by sea.
They help him to rebuild a boat stuck up in a tree in the floods, and are drawn into an dangerous race against time as the family of Mud's victim shows up to get revenge.
Director and scriptwriter Jeff Nichols admitted he borrowed freely from the novels of Twain.
"If you're going to steal stuff from somebody you should steal stuff from somebody really intelligent and I stole things from Mark Twain," he told reporters ahead of the film's world premiere later on Saturday.
"Mark Twain is one of my favorite authors and there's a scene in Tom Sawyer where Tom swims into the middle of the Mississippi River and takes a nap on the sand bar.
"I think I read that in eighth grade in English class and I just never could get it out of my head."
Jacob Lofland, the 15-year-old first-time actor who played Neckbone, said he and Sheridan noticed the similarities.
"Me and Tye got to read Huck Finn on the set ... and we found a lot of stuff that happened to wander on to the script, and we did question Jeff on that one."
Nichols chose the young actors because they were from the south of the United States and so would appear more authentic than trained performers from, say, Los Angeles.
Sheridan's first film role was in Terrence Malick's "The Tree of Life", which won the top prize - the Palme d'Or - in Cannes last year.
For Witherspoon, a best actress Oscar winner for "Walk the Line", the story had immediate appeal.
"I grew up with my brother in a creek on a dirt bike riding around, doing motocross, down in the dirt, fishing in Tennessee, so when I read Jeff's script it just felt like home.
"I never get to see home on the big movie screen and Jeff brought such an authentic, beautiful story to the place and it was just very appealing for me.
"There's very few movies about the American South that are accurate, and I feel like this is one of them."
The 12-day Cannes film festival closes on Sunday with a red carpet awards ceremony, where "Mud" and 21 other competition entries are eligible for prizes including the coveted Palme d'Or.
Critics' favorites include Michael Haneke's "Amour" (Love), Cristian Mungiu's "Beyond the Hills" and Jacques Audiard's "Rust & Bone".
(Reporting by Mike Collett-White; Editing by Pravin Char)
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