One of Scotland's leading experts on radioactive waste says warning signs should be put up at Aberdeen Beach.
Parts of the beach showed high levels of radiation
A BBC Scotland investigation has established that the level of radiation in the area could be greater than previously thought.
Professor Stuart Haszeldene said he believes the environment agency Sepa has underestimated the hazard.
Sepa however has dismissed his claims and said the risk of radiation in the sand was "negligible".
A stretch of Aberdeen Beach close to the harbour was closed for a short time in 2005.
Scotoil, a company based near the beach, has since been given two years to stop discharging waste material into the sea.
Professor Stuart Haszeldene, of Edinburgh University, said he wants it to stop immediately and told BBC Scotland he would not allow his children to play on the beach.
He added that his own independent study had found some cases where sand particles were 100 times more radioactive than would be permitted from an official radioactive site.
Traces of radiation have previously been found at Aberdeen beach
Prof Haszeldene said that while the waste was low level and presents little danger to walkers, young children or pregnant women who ate any sand particles could be at risk.
Scotoil believes a former fertiliser plant is the cause of the radiation.
Gordon McLellan, managing director, said: "If Stuart Haszeldene has concerns about Aberdeen Beach, the responsible way to raise these would be to take them in the first instance to the appropriate authorities.
"We stand by our case which we presented last year when we argued that the material found at the beach had resulted from the manufacture of fertiliser, which took place in the area in the 1960s and 70s."
A Sepa spokesman said: "Health and environmental protection are of paramount importance to us, and we know people are anxious about radioactivity on Aberdeen Beach.
"However there is no evidence presented in this report which changes our professional view that the contamination at Aberdeen Beach poses little risk to users."
He added: "Indeed it is encouraging to see that Professor Haszeldine recognises the low risk posed by this contamination. In fact he describes it as '3 times less than the radiation from a return transatlantic flight' and also 'perhaps 100 times less than driving a car'.
"Given these observations by Professor Haszeldine, we are unable to understand the basis for his recommendations."
A spokesman for Aberdeen City Council added: "The advice of Sepa is that the level of radiation is very low and that there is no public health risk.
"The council will continue to liaise with Sepa to monitor the situation and will take any necessary action as appropriate."