Dalgety Bay was the site of a World War II airfield
A Fife beach may have to be partially covered in concrete to seal radiation hotspots.
The Scottish Environment Protection Agency said 39 radioactive items were detected in September at Dalgety Bay.
It said a dose would be low for an adult, but would potentially be significant for a child.
The contamination is thought to be the legacy of aircraft waste that was incinerated and then dumped as landfill to help reclaim some coastline.
Aircraft were dismantled at a former nearby airfield at the end of World War II.
The dials in the planes were coated with luminous, radioactive radium so that they could be read at night.
Colin Bayes, Sepa's director of environmental protection, said: "In Sepa's view, the most practical solution involves breaking the pathway between the radioactive sources and the public.
"This could be achieved in a variety of ways, for example erecting clearer signage or concreting the areas where the highest concentrations of particles have been found.
"The powers to make these things happen rest with a number of the agencies round the table and we are keen to work with them all to help find the right way forward."