The exciting new research means bones collected from the ship can be matched up to see if they come from the same person.
It is hoped it will allow scientists to find out more about where the crew came from and how they lived.
Dr Garry Scarlett, a DNA expert at the University of Portsmouth, is leading the team behind the study.
He said: ‘It’s wonderful that science can help find new ways to engage people in the life of the ship, its fateful battle and in history.
‘I hope, once we have determined for certain which bones belong with which, some whole skeletons might be able to be reassembled.’
Only a handful of the ship’s 500 crew survived when it was sunk in the Solent in 1545.
Remains of about a third have been found, with the rest lost at sea.
Many bones belonging to the men - which included officers, soldiers, gunners and mariners - were found in groups, making it difficult to identify individuals.
So far 92 skeletons have been partially reconstructed through a physical study, but the new research will use molecular biology to match bones.
Earlier research allowed scientists to find out the sex of the ship’s dog, whose skeleton was also found inside the ship’s hull in 1981.
The team is working alongside maritime archaeologist Alex Hindred from the Mary Rose Museum.
She said: ‘The ability to recreate individuals from bones from DNA analysis rather than having to rely on physical matching has huge benefits.
‘Unless key parts of the skeleton of an individual are present it is difficult to associate a skull with a body, or an upper body with a lower body.
‘This technique should enable us to recreate the faces of many more of our crew.
‘Enlarging the number of re-constructed skeletons means we can tell more about them – height, age, provenance, wounds they sustained, diseases they may have had.’
The latest research is funded by charity The Pilgrim Trust.
The ship was rediscovered by divers in 1971 and excavated between 1979 and 1982.
More than nine million people have visited the Mary Rose Museum, in Main Road, to date.