Bob Olson, reeve of Cypress County, said the elk routinely jump fencing around Canadian Forces Base Suffield and then eat or trample grazing grass and crops.
Olson, who has a cattle ranch near the base, said the herd has grown from a few hundred elk in 1997 to about 6,000 animals. With no natural predators, ranchers fear the herd will continue to balloon in size, causing more damage.
"We have written letters and we have talked to the federal MPs on it but to no avail," Olson said Tuesday.
"It goes to a blind ear. They are not really listening to us."
Olson and other ranchers suggest that Ottawa should round up and kill a few thousand elk each year at the sprawling base until the herd is a manageable size. He said with a proper strategy, the herd could be reduced by as much as 90 per cent.
The meat from the slaughtered elk could be donated to food banks, he said.
"If the meat was being utilized, I don't know why Canadians would be opposed to that."
The federal and Alberta governments have been working on the problem, hoping that increased hunting will whittle down the size of the elk herd.
In 2012 the province issued 200 hunting tags for female elk. Last year the number increased to 300. This year, hunters can shoot up to 600 female elk within the boundaries of the base.
Lt.-Col. Sean Hackett, the commander of CFB Suffield, said no big cull of the herd is being contemplated.
He said the problem is complex because it involves managing wildlife that is under Alberta jurisdiction, but move back and forth from a federal base onto private land subject to provincial law.
"It is two layers of government that have to come to an understanding as to how the wildlife is going to be managed," Hackett said.
"Can I say that federal government is considering a cull? No. I can consider that a whole bunch of other folks who have responsibilities to look at the problem have to come up with an understanding of what are those targets in a given year that can be sensibly and sustainably harvested to get us to a more comfortable state."
Hackett and officials with Alberta Environment said hunting could be increased on the base in the future if herd reduction targets aren't met.
Olson said hunting alone won't do the job.
He said the big animals seem to move instinctively away from areas where there are hunters, jumping fences around the base at will.
There is also concern that large numbers of hunters will tramp or drive across ranches adjacent to the base, damaging crops and private property.
"When all of the hunters go in the base, the elk come out across the fence onto our land," he said. "If you hunt on the outside of the base, then the elk go inside the base."
The Suffield elk were brought in after 1,200 wild horses in the area were rounded up in 1994, leaving the base without a population of grazers.
The elk came from Elk Island National Park near Edmonton.
Olson said the transfer program has not been managed properly.
"If any rancher in Canada took on the job of putting a bunch of elk on their own private land and then decided that they were not going to bother managing that herd, that rancher would end up in front of a judge," he said.
Hackett said CFB Suffield will hold a town hall meeting next month so people who live near the base can bring up issues of concern, including the burgeoning elk herd.
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