WASHINGTON — The Secret Service commissioned a classified mock attack two decades ago that found an easy way to pierce the White House security zone: Overwhelm Secret Service officers on the compound with six to eight attackers climbing over the fence at the same time.

That vulnerability remains, despite the creation of specially trained counter-assault and surveillance teams recommended at the time, according to government officials who were briefed on the findings and requested anonymity to discuss sensitive information.

Securing the White House grounds has been further complicated over the past two years by severe staffing shortages and high turnover rates in the officer division tasked with patrolling the compound, according to these officials.

On Monday, federal prosecutors alleged that a man who jumped the fence and ran into the White House on Friday was keeping 800 rounds of ammunition, two hatchets and a machete in his car, which was parked blocks away.

A prosecutor also said that the man, Omar Jose Gonzalez, 42, had been arrested in Wythe County, Va., in July while carrying a sawed-off shotgun and several other firearms, as well as a map with a line pointing toward the White House. And in August, Secret Service officers saw Gonzalez near the south fence of the White House, carrying a hatchet in the back waistband of his pants. Gonzalez agreed to let the officers search his vehicle, where they found camping gear and two dogs, then released him, a prosecutor said.

Secret Service spokesman Ed Donovan declined to comment on the study or the suggestion that the White House remains vulnerable. President Barack Obama on Monday praised the agency and its officers for doing a “great job,” adding that he was “grateful for all the sacrifices they make on my behalf and on my family’s behalf.”

Still, Gonzalez’s ability to penetrate the compound reinforced deep frustrations that several Secret Service agents and officers have bemoaned with one another and friends over the past few years: Their once-elite law enforcement agency is stretched too thin and lacking the creativity to counter new threats without more bodies.

No officers on the North Lawn were apparently close enough to stop the intruder as he ran more than 70 yards from the fence to the mansion. The canine handler on duty that night did not release a dog that is trained to knock down intruders.

Rep. Jason Chaffetz, R-Utah, chairman of the House Oversight and Government Reform subcommittee on homeland security, said Gonzalez was an unsophisticated threat, but the study foreshadowed a serious one that the Secret Service now appears unable to handle. The congressman, who was not previously aware of the study, had said over the weekend that he feared what would happen “if 12 guys” all jumped the fence at the same time.

“We’re inviting more attacks,” Chaffetz said in an interview Monday. “The bad guys are paying attention. It seems the current leadership is not taking security as seriously as it needs to be in this day and age. It really scares me.”

The vulnerability study was launched in the early 1990s by Lewis Merletti, then a member of the presidential protective detail.

It was conducted by Delta Force, an elite military unit. Without knowing anything about the Secret Service’s countermeasures on the ground, the military operatives found two methods that would easily allow attackers to get inside the executive residence.

First, six to eight attackers aboard a small aircraft or helicopter could crash into the White House compound. While some would be killed in the crash or while trying to disembark, at least one or two of the attackers would make it inside the White House.

The risk of such an attack was evident about a year later, in 1994, during Bill Clinton’s first term, when a pilot crashed a stolen small airplane into the White House.

The second scenario involved at least half a dozen fence jumpers in quick succession. Officers on patrol would not be able to address every threat, the study found. At least one or two of the intruders would be able to make it into White House.

Known inside the Secret Service as the “Red Cell” study, the Delta Force work has been largely kept secret. Only the agency’s most senior officials knew of the findings, and the final report is classified.

Some of the findings were later declassified to be used for training. Several people familiar with the declassified findings said they had urged the creation of a new assault team trained to attack with deadly force and a surveillance team that would prowl the area around the White House in plain clothes to provide early detection of suspicious people.

Two people familiar with the study said not all of the recommendations were adopted for handling a swarm of fence jumpers. These people said they were not at liberty to describe the security gaps in detail because much of the report remains classified.

Dan Emmet, a former member of the Secret Service’s early counter-assault team, said he and colleagues were stunned by the Friday breach and called it a new low.

“This particular incident is a tactical failure. The Secret Service cannot spin this or minimize it,” Emmet said. “The only thing I can imagine is there were no uniform division officers in that area when he happened to do that. And that is ridiculous.”

Adding to the challenge at the White House has been a staffing shortage.

Seeking to save money amid budget constraints since 2012, the Secret Service decided not to fully staff its uniformed division, which is tasked with protecting the White House complex. The agency is authorized to employ 1,420 officers but has been down between 40 and 100.

At the end of this year, the service expects to have 1,346 officers on staff in the uniform division.

Filling vacancies has been difficult in part because the agency director agreed in 2012 and 2013 to cancel all but three Secret Service academy classes. The classes, which handle 24 students at a time, create a ready pipeline of recruits — but the cancellations have restricted the flow.

Morale has plummeted as uniform officers are routinely asked to work on their off days; they complain of not being paid proper overtime for the extra shifts.

“Hard decisions had to be made, based on the facts at the time,” said Donovan, the Secret Service spokesman. “There is not an endless amount of money. We can’t do the hiring, and that’s the decision that was made.”

But Donovan said the agency is moving to try to catch up and train a new set of recruits, and Secret Service Director Julia Pierson has plans for 11 new academy classes this summer.

“The director has a plan in place. We want to be fully staffed in 2015,” Donovan said. “There’s a hiring strategy in full motion.”

On Monday, the House Oversight and Government Reform subcommittee on homeland security called a hearing for next Tuesday and for Pierson to answer questions about the security breach.