Finding an apartment in Manhattan can be tough. Just ask the Metropolitan Transportation Authority.

Next year, dozens of New Yorkers in some of the city’s wealthiest ZIP codes are set to be evicted to make way for the long-delayed Second Avenue subway, and federal law requires the transit agency to find them comparable new homes. So far, it has not been going so well.

Dave Zigerelli was told to consider low-income housing across from an on-ramp to the Queensboro Bridge. The first apartment shown to Nicolle Poian was half the size of her own. Ann and Conrad Riedi, ensconced in the same rent-stabilized apartment for 40 years, said they were encouraged to move out of Manhattan  and their dog, Biscuit, might not be allowed to come along.

“They told us to think outside the box,” said Ms. Riedi, 64.

The Riedis’ apartment, a big three-bedroom in a stucco-walled walk-up, is one of 60 homes on the Upper East Side that will soon be converted into ventilation shafts, public stairwells and electronics hubs, the infrastructure for the $4.5 billion underground line, scheduled to open in 2017.

The transportation authority said that it was doing its best to accommodate residents who want to stay in the neighborhood, and that no one was being forced to leave the area. Affordable housing was suggested to residents who might be eligible, said a transportation authority spokesman, Kevin Ortiz.