The research, led by Dr Peter Campbell at the Wellcome Trust Sanger Institute, may also help doctors identify if a patient's cancer has been caused by radiation, and change how the cancer is treated.
Ionising radiation, such as gamma rays, X-rays and radioactive particles, can damage DNA, which in turn can lead to cancer. But before this research, scientists didn't know how the damage happens.
The researchers compared the DNA in secondary radiation-associated tumours from 12 patients with the DNA in other types of tumour from 319 patients. They found two characteristic patterns of damage in the DNA of the radiation-associated tumours, which were independent of the specific type of cancer.
The first was a deletion, where small numbers of DNA bases had been cut out.
The second was a balanced inversion, where the DNA had been cut in two places, the middle piece had spun round, and then joined back again in the opposite direction. Balanced inversions are normally extremely rare, but might happen if high-energy radiation causes enough breaks in the DNA at the same time to make them possible.
Dr Sam Behjati, a clinician researcher at the Sanger Institute, said: "Radiation probably causes all types of mutational damage, but here we can see two specific types of damage and get a sense of what is happening to the DNA."