The vacancy rate among mammographers who specialise in breast exams is 17.5%.
Among mammographers who assess women who have found a lump or have a family history of breast cancer, the vacancy figure is 20%.
Sue Johnson, who represents the SoR, told the BBC: ‘The role of the radiographer has developed and evolved and there is a much broader scope to the job role than simply taking the images.
‘It's a very desirable and enjoyable career and men are saying we would like to access that same career and we could help deliver the service.'
The prospect of men performing mammograms has been explored unsuccessfully in the past, but ‘the world has changed', said Johnson.