Directed by Take Shelter helmer Jeff Nichols, the drama centres on two young boys who meet a fugitive (Matthew McConaughey) being pursued by a bounty hunter.
The boys (Tye Sheridan and Jacob Lofland) help McConaughey to hide, in the hopes of reuniting him with his long-lost love (Reese Witherspoon).
The trailer, released by Yahoo! Movies, also features Take Shelter star Michael Shannon, Sam Shepherd and Sarah Paulson.
Mud played at last year's Cannes Film Festival, where it was nominated for top festival prize the Palme d'Or.
Mud will be released in the US on April 26, with a UK release date yet to be confirmed.
Watch Michael Shannon discussing Take Shelter with Digital Spy below: