No negotiations were scheduled between the two sides, although a mediator from a state labor board was meeting with both union and MTA officials Tuesday afternoon.

The MTA asked the Public Employment Relations Board to formally declare an impasse, the first step toward forcing binding arbitration of the contract, said James Edgar, the board's executive director.

It was the city's first transit strike since an 11-day walkout in 1980, which happened in much warmer April weather. The effect this time, however, was tempered by the advent of personal computers, which enabled many commuters to stay home and work via the Internet.

Others boarded water taxis along the Hudson River, or jumped into carpools. Many lined up in the cold to await private buses arranged by their employers, or shared yellow cabs with strangers. There was a minimum $10 fee for cab riders.

"The city is functioning, and functioning well considering the severe circumstances," the mayor said. The union "shamefully decided they don't care about the people they work for, and they have no respect for the law. Their leadership thuggishly turned its back on New York City. This strike is costing us."

Jack Akameiza, 66, was trying to figure out a way to go the nine miles from Manhattan to Coney Island. "I cannot go to work," he said. "I cannot take care of my family."

Some commuters were upset at the union, others with management. Some, as they made their way to work, blamed both sides.

"It's two arrogant groups not caring that 7 million people are inconvenienced," said Kenny Herbert, 45, of Brooklyn, who took the train to work Monday night but needed a water taxi across the East River to get home.

The International TWU, the union's parent, had urged the local not to go on strike. Its president, Michael O'Brien, reiterated Tuesday that the striking workers were legally obligated to resume working. The only way to a contract, he said, is "not by strike but continued negotiation."

The first day of the strike was expected to cost the city $400 million in revenue, with an additional loss of $300 million per day afterward, according to the city comptroller's office. Countless stores and restaurants were affected.

The mayor put into effect a sweeping emergency plan, including a requirement that cars entering Manhattan below 96th Street have at least four occupants.

Lorraine Hall came to New York expecting a lighthearted celebration of her 65th birthday, but the lack of mass transit put a damper on the occasion. She was determined to make the best of it until her departure on Friday.

"I didn't come up here to sit in a hotel room, and as long as my two feet are letting me push it, I'm going to push it," said Hall, who lives in Lancaster, S.C.

The union said the latest MTA offer included annual raises of 3 percent, 4 percent and 3.5 percent. Pensions were another major sticking point in the talks, particularly involving new employees.

Union local president Roger Toussaint said the union wanted a better offer from the MTA, especially when the agency has a $1 billion surplus this year.

The contract expired Friday at midnight, but the two sides had continued talking through the weekend.