The Irish Whale and Dolphin Group wants the Army to train members to shoot stranded whales when there is no hope of getting them back to sea.
The proposal is part of a draft protocol the charity is preparing in a push for a more co-ordinated and humane approach to whale strandings.
Seven northern bottlenose whales died on Rossnowlagh beach in Co Donegal last week in the largest stranding of its kind in Ireland.
Volunteers from the Irish Whale and Dolphin Group (IWDG) had to issue appeals to the public to give the animals space to die in peace after selfie-seeking crowds gathered on the beach and concerned animal lovers demanded rescue attempts.
Simon Berrow, chief science officer with the IWDG, said neither group fully understood the situation.
"People are naturally curious and very well-meaning, but there was no possibility of refloating the whales, and we were trying to minimise their distress," he said.
"Even if they could have been moved without harming them and brought out to sea, they live in waters 2,000m deep, 150 miles away. Donegal Bay is not the place for them.
"One refloated when the tide came in before being washed up again and people wondered why more wasn't done for him, but we're a charity and we don't have the kind of equipment that might be of use.
"We also believe this was a family group and he was an immature male who wouldn't survive without them, so it would have been prolonging his suffering."
In some countries, a powerful drug, Immobilon, is used to euthanise stranded whales and other sea animals that can not be saved, but it is not licensed in Ireland.
"It also needs a vet to administer it and it takes specialist knowledge to find the right place to inject," Mr Berrow said. "Then there's a problem if birds or other animals get to the carcass, because a tiny amount will kill.
"The other option is humane shooting, but we need the Army for that. We need to work out the ballistics, have personnel trained in knowing the right spot to shoot and have people ready to set up cordons, because you have to have a very wide exclusion zone. We've been working on a proposal for a while, but we need the Defence Forces, the National Parks and Wildlife Service (NPWS), the Department of Agriculture, and probably other agencies around the table to discuss it," he said.
Live whale strandings are rare in Ireland, but there have been three so far this year. There have also been 21 live dolphin and porpoise strandings, while 198 dead specimens have been washed up.
The response often depends on what volunteers are available and whether they can round up local vets and find transport and Department of Agriculture facilities to take samples or carry out post-mortem examinations.
"There are opportunities to learn from these strandings, but it's very hit and miss as to whether we can do anything other than get photographs. If there was a national protocol in place, more could be done," Mr Berrow said.
The Department of Defence carries out operations for the NPWS under an arrangement due for renewal next year.
"Any additional request for support from the Defence Forces will be reviewed in the context of the new agreement," it said. The NPWS was asked for comment.