Generation X and baby boomer homeowners in the Bay Area are considerably more opposed to construction of new housing in their neighborhoods than millennials and those who have moved to the region in the last few years.

Moreover, a greater number of newer residents are worried about whether they can find affordable homes in the region than those who have lived here for many years.

That’s the bottom line, according to a new poll released Sunday by the Bay Area Council showing generational divides in residents’ attitudes toward the region’s housing crisis. Among millennials — ages 18-39 — 70 percent say “yes” to new housing in their neighborhoods. But only 57 percent of residents age 40 and older support such housing.

A majority of residents — 62 percent overall — supports putting new housing in their neighborhoods, up from 56 percent in 2014.

Attitudes are “trending in the right direction, and I think it’s a reflection of the severity of the housing crisis,” said Matt Regan, the council’s senior vice president of public policy and government relations. Still, he said, too many older homeowners continue to “kick as hard as they can at anybody else trying to get on their ladder.”

A separate poll released Thursday by the council showed that 40 percent of Bay Area residents — and 46 percent of the region’s millennials — are considering leaving the region because of congested roadways and exorbitant housing costs. Those costs have marched higher in recent years as the local economy has generated more jobs while the supply of available housing has shrunk.

Sunday’s poll reveals that 80 percent of millennials say they are concerned about finding an affordable place to live, as opposed to 52 percent of those in the 40-64 age bracket and only 36 percent of those 65 and older.

Many older homeowners, Regan said, have “for all intents and purposes built regulatory walls around their communities that prevent even their own children from moving back to the area after college, given the housing costs.”

By supporting local zoning barriers to development, he contended, entrenched homeowners have helped create “a ticking time bomb. If we don’t have a course correction, we’re going to end up with a very old region without enough new taxpayers to pay for our transportation infrastructure, our schools, our hospitals, all the services we need.”

The council drew its conclusions from the polling of 1,000 registered voters in the region’s nine counties: Santa Clara, San Mateo, Alameda, Contra Costa, San Francisco, Marin, Sonoma, Napa and Solano.

The poll shows more new Bay Area residents worry about finding an affordable home than those who have lived here the longest: 81 percent of those living here for five years or less share that concern, compared with 69 percent of residents here 6-10 years, 64 percent of those in the region 11-20 years and 48 percent of those with 20 or more years in the region.

There are county-by-county differences, as well. When it comes to supporting new housing in one’s own neighborhood, 64 percent of those in San Mateo County say “yes,” while 60 percent agree in Santa Clara County. In the East Bay, 61 percent support new neighborhood housing in Alameda County, but only 49 percent support it in Contra Costa County, which is more uniformly suburban.

Developer Kevin Casey, whose Emeryville-based company, New Avenue, specializes in building accessory dwelling units — so-called “granny units” — said attitudes have “turned a corner” as awareness of the crisis has grown.

“We haven’t had a neighbor fight an accessory dwelling project in two or three years now,” Casey said. “In fact, we see politicians who get up and say, `We’re going to build thousands of backyard cottages,’ and they get cheered.”

Lenny Siegel, a Mountain View City Council member and housing advocate, said, “People who have children who can’t buy homes are beginning to realize that though they’ve made it, they want their children to be able to live nearby. And the corollary is, how far do you have to travel to see your grandkids?”

That said, he expressed some empathy for homeowners concerned about neighborhood development: “Some of the reasons people are concerned about it are valid: traffic, parking … and will you put up El Capitan or the Tower of Pisa in somebody’s backyard?”