A report from the National Cancer Registry Ireland has suggested that the risk of men developing lung cancer may now be levelling off, after a steady rise in cases since 1994.
NCRI, however, suggests that overall, the total number of cancers continues to rise.
This is mainly due to the ageing population.
The report says that while the risk of lung cancer continues to fall for men, due to a long-term fall in the number of men who are smokers, the risk is still increasing for women.
It says that lung cancer was the leading cause of cancer death in both sexes, accounting for 18% of cancer deaths in women and 23% of cancer deaths in men during the period 2011-2012.
Deaths from lung, colorectal, breast and prostate cancers combined made up almost half of all deaths from cancer during this period.
Speaking on RTÉ’s Morning Ireland, Dr Harry Comber, Acting Director at the NCRI, said: "We see that the rate of lung cancer for men has been falling for a number of years and that is the main contributor [to falling cancer rates in men].
"The other thing we've seen in the last few years is that there's had been quite a massive increase in the rate of prostate cancer diagnosis and that seems now to be levelling off.
"Those are the two main cancers in men and those are the two which show the greatest signs of decrease at the moment."
However, he said a big increase has been noted in melanoma, particularly in men, which is due to sun exposure 15-20 years ago.
He said people are still a bit casual about sun exposure, particularly about sunburn.
Dr Comber said people are very careful about their children but possibly less careful about getting sun exposure themselves.
He said it is important to stress that excessive exposure to sun, especially sunburn, can be fatal.
There has also been an increase in mouth and liver cancers.
Dr Comber said the increase in mouth cancer is mainly as a result of smoking but in recent years the sexually transmitted virus, human papillomavirus, is also a contributor to the increase.
He says it is not very clear why there has been an increase in liver cancer, which he said is not the main form caused by alcohol exposure.
He said the increase is also being seen in many other countries but the reason is as yet not known.
A leading oncologist has said cancer is primarily a disease of the middle aged and elderly, so as life expectancy increases there is an inevitable upward trend for cancer cases.
Speaking on RTÉ's Today with Sean O'Rourke, Professor John Crown said the decline in smoking related cancers is very encouraging.
He said better drugs and treatment are leading to much improved outlooks for cancer patients.
Prof Crown said better drug treatment is responsible for the increased survival rate in breast cancer and that mammography, while important, is not as significant in the reduction of breast cancer cases.
He said that while the treatment for bowel cancer has improved dramatically, real efforts should be made in 2016 to ensure no one has to wait more than a few weeks for a colonoscopy.
He added that melanoma is a real emergency in this country and we do not have proper access to new treatments.
Prof Crown said one type of cancer treatment does not fit all and this is changing with increasingly sophisticated means to analyse what particular type of cancer a patient has and how to treat it.