Bay Area apartment rents reached a record high in the second quarter, according to a report Tuesday, continuing a three-year run of steady increases that’s setting off alarms among economists and corporate leaders.

Rents averaged $2,158 a month in the nine-county Bay Area, a nearly 20 percent gain since the second quarter of 2011, and a 10.3 percent jump from the same period last year, according to Novato-based RealFacts. Rents were up 5.6 percent from the first quarter.

Alameda County saw the biggest percentage gain — up 12 percent from a year ago to an average rent of $1,928 a month. The area’s under pressure partly because of refugees from San Francisco, where rents averaged $3,229 in the second quarter, a 9.4 percent annual gain. The San Francisco metro area has the highest rents among the country’s 25 largest rental markets, according to online real estate site Trulia.

The average apartment rent was up 9 percent to $2,321 in Santa Clara County; up 8 percent to $1,609 in Contra Costa County and up 8.1 percent to $2,470 in San Mateo County.

A limited supply and strong demand are responsible, economists and housing experts say. They worry that continued job growth in the region — boosted by the remarkable boom in tech — is unsustainable without similar growth in housing.

“All of these companies are hiring and new people are coming in from around the world and around the country,” said Stephen Levy of the Center for Continuing Study of the California Economy in Palo Alto. “They’re good jobs and they’re bidding against a limited supply of apartments. It’s both a sign of strong job growth and a sign we need to give it attention.”

Jim Wunderman, president and chief executive of the Bay Area Council, said the region needs to work together to build more housing.

“There needs to be a partnership between cities, counties and companies to get housing built fast so that we can enable the growth pattern to continue,” he said. “Otherwise, it forces labor costs up because a company has to pay more because of the rising cost of living. They’ll do that for a while, but eventually they’ll start looking for alternatives.”

Housing has consistently been the top concern in a survey of corporate executive members of the Silicon Valley Leadership Group, said Shiloh Ballard, the group’s housing analyst. “We’re not achieving the number of homes to keep pace with demand, and we see that with increased rents.”

The relentless gain in rents has people such as single mom Waynetta Mills, an insurance agency account executive who lives in Dublin in the East Bay but works in San Mateo on the Peninsula, planning to lengthen her commute.

“As a single mother of two, I have no choice but to move farther out to be able to afford to live,” said Mills, whose rent for a two-bedroom apartment in Dublin was just raised 9 percent to $2,180 a month.

“I’m not looking forward to commuting from the Suisun-Vallejo region all the way to San Mateo, but at this point I really have no choice,” she said.

Linda Nichols, who operates a day spa in Menlo Park, struggled to find another apartment after receiving a 60-day move-out notice from new owners.

“I was born and raised here, but honestly I don’t know how much longer I’m going to be able to stay,” Nichols said. “It’s sad. I’m going to have to sell a good business.”

Nick Grotjahn of RealFacts said that “for apartment owners and developers this is all good news, but for renters and especially your average renter in the Bay Area, not your high-tech worker, it’s really putting the squeeze on you.”

RealFacts measures rents in apartment complexes and townhomes of more than 50 units, so the prices — which are averages of all sizes of apartments — tend to be higher than for smaller developments.

Ron Stern of Bayrentals.com, which lists smaller complexes and houses for rent around the Bay Area, said he’s seen rents increase 20 percent in the past few years. “Even apartment managers are shocked at what they have to charge in rent now,” he said.

RealFacts said Bay Area apartment rents in large complexes ranged from an average of $1,859 for a studio to $2,868 for a two-bedroom, two-bath apartment and $3,258 for a three-bedroom townhouse.

According to RealFacts, San Jose had an average apartment rent of $2,169, Oakland $2,421 and Concord $1,418.

Patricia De La Torre, who works for a semiconductor company and lives in a three-bedroom townhouse in Mountain View, is looking for a second job “just for the extra spending money.” Two of her sons have graduated from high school but the other two are still in school and her rent is nearly $3,000 a month. “It’s so hard to balance everything out,” she said.

Ruben Holmes left San Jose after 30 years there and moved to Mountain House in San Joaquin County where he rents a five-bedroom, three-bath house for $1,600 a month.

“I never thought I would leave San Jose,” said Holmes, who has an Internet business and works from home.

Effie Moore of San Jose said she knows people who are moving to Sacramento and Patterson in the San Joaquin Valley.

“I never heard of Patterson until I had friends moving there,” Moore said. “I’ve seen a lot of people moving out of the Bay Area. A lot of friends are moving to Sacramento, and that’s what we’re going to end up doing so we can buy a home.”

Contact Pete Carey at 408-920-5419. Follow him at Twitter.com/petecarey.