The pair can be seen in period dress on the set of the movie, which is directed by Susanne Bier (Things We Lost in the Fire).
Serena stars Lawrence as the titular character, who moves into the North Carolina mountains with her husband George Pemberton (Cooper) in 1929, building a powerful and ruthless timber empire.
But when the strong and independent Serena realises that she can never bear a child, she sets out to have revenge on her husband's illegitimate son.
"2929 is thrilled to bring Ron Rash's epic American novel to the big screen," said producer Ben Cosgrove.
"Audiences are drawn to great stories with authentic characters - with this amazing cast and a director of Susanne's calibre at the helm, we're confident that moviegoers will find Serena riveting."
The film is based on Rash's acclaimed 2008 novel of the same name.
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Serena will also star Toby Jones and Rhys Ifans. Christopher Kyle (Alexander) wrote the screenplay.
A release date is yet to be set for Serena.