BOSTON — The Massachusetts Bay Transportation Authority suspended all rail service on Monday because of an unprecedented onslaught of snow, prompting the cancellation of all Amtrak Downeaster trains on Tuesday.

The MBTA said all subway, trolley and commuter rail trains would be shut down at 7 p.m. Monday and there would be no service all day Tuesday as crews scrambled to clear snow and ice from tracks and assess the damage the recent storms has done to equipment.

Buses would continue running, officials said, but only on a limited basis.

A notice posted on the Downeaster’s website at 9 p.m. Monday said the MBTA’s supension of service “has forced the Downeaster to cancel all trains as well as there is no way for our trains to enter” Massachusetts.

The Downeaster runs five round trips between Maine and Boston on weekdays, and said on its website that it plans to resume normal service Wednesday.

The storm that began during the weekend left more than 20 inches of snow in Boston and many surrounding communities, adding to a record amount of snow that had fallen over the past 30 days.

Massachusetts Gov. Charlie Baker said the performance of the MBTA was unacceptable and he planned to meet with transit officials after the latest storm to discuss service disruptions.

Early Monday, nearly 50 commuters had to be evacuated from a disabled Red Line train in Quincy after being stranded for more than two hours. No one was injured. Officials said the train lost connection to the electrified third rail because of the buildup of snow on the tracks.

Baker said his administration spent a lot of time during the weekend talking to public transit officials to make sure they could run an at least a scaled-back schedule during the latest storm.

“We’ve been disappointed by the fact that even that abbreviated schedule hasn’t been able to be maintained. Once it stops snowing, we plan to have a long conversation with the folks at the T about improving performance,” Baker said. “There are a lot of people at the T who I know have been working extremely hard, but this performance is simply not acceptable.”

After the announcement that rail service was being suspended, Baker said transit officials made the right call if they believed they could not deliver adequate service on Tuesday. The MBTA is a semi-independent agency and not under direct control of the governor.

Officials at the transit agency say aging equipment has exacerbated the weather-related problems, which have delayed and angered many riders.

At the T’s Red Line station in Cambridge’s Kendall Square, near the MIT campus, riders said they were more or less prepared for a long slow commute Monday, especially given the challenges the subway line faced last week.

Valerie Patilla said her morning commute from Boston’s Hyde Park neighborhood lasted about an hour and a half – more than twice as long as her normal commute, which also includes a subway transfer and a bus ride.

“But this was a good one. Last week it took two and a half hours,” she said as she waited for a train home after being let out of work early. “That was awful. I sum it up as leading cattle in a herd.”

Cassie Smith, of Boston, said a delay on the Red Line earlier Monday had forced her to cut short her doctor’s appointment.

“I only got to see him for 10 minutes, so I’m just really frustrated,” she said as she headed back into Boston’s Beacon Hill neighborhood. “It said it was arriving in 15 minutes but took a lot longer. I could have walked across the river faster if I had known.”