Prime Minister Mark Carney admitted last week that he has prepared for a once-unthinkable scenario - a US invasion.

Noting the risk was low and the likelihood highly improbable, he told the New York Times he had a responsibility to consider all possibilities as the US-Canada relationship is redefined under the Donald Trump presidency.

"That's just risk management," Carney said.

Trump's global tariffs and his often-repeated desire to make Canada the 51st state has led Canada to war game an attack by the Americans.

In 2025, the US president said it was "highly unlikely" that the US would ever use force against Canada. Instead he said, he would continue to exert economic pressures to obtain political aims.

"President Trump has done more than anyone to protect the great people of Canada," the White House told the BBC in a statement this week.

Military experts who spoke to the BBC also think an invasion is a long shot, pointing to the multiple ways the two countries work together on defence.

But the issue is clearly weighing on Canadians' minds.

In January, after the US captured Nicolás Maduro in Venezuela, a Leger poll suggested that over 30% of Canadians believed that a US invasion was likely.

A war between Canada and the US would be complicated and almost difficult to imagine, said Lt-Gen Christopher Coates, a former military officer of 34 years with the Royal Canadian Air Force who held various senior positions.

"I was involved in military operations for my whole career, and we never considered the possibility that there would be a military attack coming from US territory," he told the BBC.

Coates, who had served on Nato missions, noted that Canada and the US collaborate on many aspects of military defence.

They are both members of the north Atlantic defence alliance, which mandates members to defend a fellow member-nation should they be attacked.

The two countries also conduct joint Arctic defence missions under the North American Aerospace Defence Command (NORAD), and frequently share intelligence.

Because of this, Coates said he believes an attack by the US on Canada would not begin with an armed assault, but rather with more discreet means like cyberwarfare.

After World War II, Canada and the US became natural allies for the latter part of the 20th Century, and have become heavily integrated economically, militarily and culturally.

But it wasn't always this way. In fact, a core tenet of Canada's identity is its resistance of US expansionism in the 18th and 19th Centuries, said Tim Foran, a researcher with the Canadian War Museum.

"Fear of the United States is foundational to the political project that is Canada," he said.

Canada was formed as a collection of British North American colonies who remained loyal to the British Crown when the colonies in the modern-day US rebelled.

Before the formation of Canada, the US had attempted to invade British North American colonies, taking control of Montreal in 1775 and nearly conquering Quebec City.

In the war of 1812, the Americans invaded what was known then as Upper Canada, Lower Canada and the maritime colonies repeatedly, resulting in a stalemate. During that war, British troops famously burned down the White House in retaliation.

Foran said that at the time, the colonies that later became Canada relied on Great Britain and its Royal Navy for its defence, as well as indigenous peoples who served as generals in major battles.

Canada again contemplated war with the US post-World War I in response to its growing power and influence.

It drafted a plan that was informed by secret trips to border cities made by Canadian army generals, who would pose as tourists and snap photos of bridges and highways for intelligence.

They also spoke to local residents to better understand their enemy.

A war was an unlikely scenario then, said Andrew Burtch, a researcher with the Canadian War Museum with expertise on Canada in the 20th Century, but the Canadians still wanted to be prepared.

"That's part of what militaries do," he said. "They envisage all sorts of different scenarios."

Even if a US invasion is extremely unlikely, Matthew Schmidt, an associate professor of national security at the University of New Haven in Connecticut, said the fact that Canadians were preparing was a sign of just how drastically the global order has shifted.

He added Canadian leaders do have hard questions to ask about how closely they want to continue working with the American military - a partnership that gives them valuable information should they want to harm Canada in any way.

"It's really doing harm to relationships with the United States, and there's a certain amount of legitimate fear," he said.

Americans might not take Trump's comments about making Canada the 51st state seriously, he said, but Canadians clearly do - and are prepared to defend themselves if needed.

So what would it be like if it happened?

The first phase of a war could be quite short.

According to the model used by the Canadian military, as reported on by the Globe and Mail newspaper earlier this year, a US attack would see Canada's strategic positions overwhelmed within a week

Its military would quickly be outnumbered, forcing Canadian forces to resort to guerilla-type warfare to try to suppress their enemy.

Allied nations like France and Britain would be called on to provide support and defence for Canada, the newspaper reported in January, citing senior government officials.

The theoretical model is believed to be the first time in a century that Canada planned for an American assault.

The modelling is on the lighter end of military combat planning, Coates said.

He said that Canada, unlike its Nato allies, was lagging behind when it came to having a response plan in place in the event of any ground invasion, and that it was now playing catch-up in this era of unpredictable geopolitics.

Part of that, he said, was made evident by a recent call by Canada's defence chief to drastically increase the size of its military, including the addition of as many as 300,000 lightly trained citizen soldiers.

An invasion of Canada might not be straightforward from the US point of view either.

Even with its outsized military, the US would have a difficult time getting buy-in for a fight with Canada, said Schmidt.

"I think you would have a large number of American officers who would resign if given the order to invade Canada," he said.

"They would see it as an illegal and immoral order."

Schmidt said Canadian soldiers and American soldiers routinely train together, and share a mutual respect.

But in the unlikely scenario that relations would deteriorate to the point of combat, Schmidt said the US would likely focus on acquiring valuable Canadian resources like oil and minerals, and political decapitation.

"You would see a a kind of operation that would mirror perhaps what you saw in Venezuela," he said, referring to US military action earlier this year to capture former Venezuelan President Maduro.

Although he acknowledged the US has greater military capacity, he said that "pound for pound" Canadian soldiers would be able to put up a fight.