The Office star married Yeoman in December 2006.
"Lucy and Owain have been rowing all the time, mainly because his career has really started to take off so he has been away from home a lot filming," a source told the News Of The World.
"Right now she is a bit down and her weight has gone up. Everyone is hoping they can get things back on track."
The insider continued: "Owain's family were out visiting recently and witnessed how much strain their marriage is under and how unhappy Lucy is. They said she was just not herself and seemed vacant and sad."
A representative for Davis made no comment on the rumours.