The babies were an average age of seven months.
The researchers state that while most mothers feel stressed during the early stages of their baby's life, their cradling habits can be a key indicator of whether this stress could become overwhelming and lead to depression.
As a part of the study the researchers asked mothers to pick up their babies and cradle them in their arm.
They women were then asked to complete a survey that quizzed them on their mental state.
The study found that of the mothers who expressed no signs of stress or depression in the survey, 86 per cent preferred to hold their babies to the left.
However, cradling babies to the right was more prominent amongst stressed mums with 32 per cent showing a right-sided bias.
Lead author Dr Nadja Reissland, a senior lecturer with Durham University's Department of Psychology, said early detection of stress is vital.
"Many mothers don't realise they are suffering from stress, or don't want to admit they are. The way they interact with their child is usually the best indicator of their inner mental state," she said.
"Mums who are stressed often see what their baby does as negative so they may interpret their baby's crying as being naughty, when in fact this is normal behaviour. They may even feel the baby is stopping them from living the life they really want to live.
"These sorts of feelings can have a huge impact on the relationship between mother and baby and on the family as a whole. If this stress develops into depression, then the situation can be even worse."
Funded by the Children's Research Fund, the study appears in the on-line version of the Journal of Child Psychology and Psychiatry.
The research team now is following up this pilot study with another study looking at cradling side in a before and after situation with mothers taking their babies for their first vaccinations.