CBS News/ May 13, 2011, 10:18 AM

Tilda Swinton earns early praise at Cannes for "We Need to Talk About Kevin"

Tilda Swinton attends the "We Need to Talk About Kevin" premiere during the 64th Cannes Film Festival on May 12, 2011, in France

/ Getty Images

(CBS/AP) -- British actress Tilda Swinton and her new film, "We Need to Talk About Kevin," may be the one to beat for top honors at the Cannes Film Festival.

Directed by Lynne Ramsay and based on the acclaimed novel by Lionel Shriver, the film is about a teenager who commits a school massacre, and his mother's bottomless grief.

Pictures: Cannes Film Festival
Pictures: Tilda Swinton

"There's no violence in this film," Ramsay told reporters after the film's first Cannes Film Festival screening. "You only see aftermath. Every Hollywood movie is more violent than this."

Swinton stars as Eva, an American middle class mom numb with grief and guilt, constantly replaying her son's childhood for clues about why he went on a murderous spree - and whether it is her fault.

Swinton, whose unflinching performance makes her an early favorite for the Cannes' best actress trophy, said the character is haunted by the idea that in her son she is "giving birth to her own violence."

"It's like a nightmare scenario, but it's not that far from the everyday experience of being a parent," said Swinton, an Academy Award winner for 2007's "Michael Clayton."

"It's a bloody business, having a family," said Swinton, the mother of teenage twins. "It's certainly a very bloody business being a parent, and it's a really bloody business being a child."

The film also stars John C. Riley, as Swinton's well-meaning husband, and 18-year-old Ezra Miller as her son.