As the stock market was having its worst day in 30 years on Thursday, customers at a Bank of America branch in Midtown Manhattan, the financial heart of New York, were lining up to take cash out of their accounts — sometimes tens of thousands of dollars at a time.

So many people sought huge sums that the bank branch, at 52nd Street and Park Avenue, temporarily ran out of $100 bills to fulfill large withdrawals, according to three people familiar with the branch’s operations. The shortage hit after a rash of requests for as much as $50,000, said two people who witnessed the rush.

The problem was limited to large bills — the bank’s A.T.M.s stayed stocked and customers with routine transactions were still able to take out cash. By Friday morning, the bank had refilled its supply of big bills, two of the people said.

But the desire for cash persisted: A teller at a JPMorgan Chase branch across the street said on Friday that there had been a “nonstop” stream of customers stockpiling cash over the past two days.

Bill Halldin, a Bank of America spokesman, said the bank had enough cash available at its branches meet its clients’ needs. “We don’t keep large amounts of cash in big bills in the branches because it’s dangerous for our employees and there is low demand,” he said.

Even so, it appears the deep level of fear that has set in on Wall Street — as weeks of market gyrations have wiped trillions of dollars of wealth — has also permeated people’s personal lives.

This week, the coronavirus pandemic ended one of the longest bull markets in history. The S&P 500 stock index tumbled nearly 10 percent on Thursday — its worst day since the Black Monday crash of 1987 — ending a mostly steady upward climb that lasted 11 years. The market closed the week on a higher note after President Trump declared a national emergency, freeing billions in funding to fight the epidemic.

Most people use far less cash than they did even a decade ago, as credit cards and other forms of digital payment have become the norm. Still, stacks of bills are psychologically reassuring, and are often what people, even the wealthiest, turn to in an unpredictable world.

The Park Avenue bank branches — just steps away from the headquarters of MetLife and BlackRock, the world’s biggest investment management firm — draw an unusually affluent clientele. The typical American household has around $4,500 in its bank accounts, according to a SmartAsset analysis of the latest Federal Reserve data.

Industry officials said the banking system had plenty of cash available to deal with a surge in withdrawals.

Banks keep much of their cash in giant vaults, some maintained directly by the Federal Reserve, and manage their daily cash supplies by ordering deliveries through secure-transport services.

One of the biggest cash haulers, Brink’s, had “a big spike in demand” this week from some of its bank clients, according to Edward Cunningham, a company spokesman. “They’re putting more cash into branches, they’re requesting more frequent replenishment of A.T.M.s.”

The Fed has not experienced pronounced increases and has “had no difficulty meeting demand,” a Federal Reserve spokeswoman said. She added that the central bank had plans in place to address a range of contingencies.

In East Rutherford, N.J., a storage facility operated by the Federal Reserve Bank of New York keeps billions in custody for banks in the area. It is accustomed to dealing with surges — holidays and long weekends, for example, can send demand up by 20 percent — and it has the capacity to more than double its shipment volume if needed, according to two people familiar with its operations.

So far, demand there this week has been within fairly normal levels, and is far short of the surges experienced around Hurricanes Maria and Sandy, one person said.

Other systemic shocks have led to brief jumps in cash demand. In the days immediately after the Sept. 11 terror attacks, the supply of cash in circulation rose by $4 billion, a Federal Reserve Bank of Richmond study found.

Banks and their trade groups have been on conference calls all week with officials from the Federal Reserve and other government agencies, including the Centers for Disease Control and Prevention, about the industry’s efforts to deal with the fallout from the coronavirus outbreak. The topics have included how to handle a rash of mortgage refinancing applications and tips for disinfecting high-touch surfaces like A.T.M.s.

At Brink’s, Mr. Cunningham said the uptick in cash requests had so far come mainly from the biggest banks and might taper off as more customers hole up in their homes.

“I don’t know how long it will persist,” he said. “It’s kind of hard to predict what’s going on right now.”

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