The Institute said it did not know the reason why the whales washed ashore.
It added that "The most humane way to perform euthanasia on whales is to shoot them through the brain, and this was successfully performed on those whales suffering on the beach.
"We wish to stress emphatically that the most humane effort was employed to prevent further suffering of these animals."
The marine mammals weigh between four and five tonnes and measure up to 5.5 metres.
Some volunteers who tried to get the whales back into the sea had to be rescued themselves because they were carried away by strong waves.