According to the National Enquirer, the babies are said to be suffering from colic, a common but largely unexplained condition that causes repeated episodes of excessive and inconsolable crying.
Sources claim that the Tomb Raider star is struggling to cope with the twins' constant state of distress and has slipped into "depression mode", raising fears that she may be suffering post-natal depression.
"The 33-year-old has been trying to control her emotions" around her older children Maddox, 7, Pax, 4, Zahara, 3, and Shiloh, 2, but "her mood swings have been hard on the entire family," according to the source.
"She has been staying in bed most of the time, all she does is sleep. She has little energy and has to force herself to remember to eat because she is still breast feeding," the Daily Telegraph quoted the source, as telling In Touch magazine.
"She cries at the drop of a hat and laughs at inappropriate times," the source added.