Georgia universities and companies are rushing this week to apply for U.S. visas that will allow them to hire overseas workers with skills in science, technology, engineering and math.

The Homeland Security Department annually makes available 85,000 visas nationally. That is a fraction of the work permits the science and tech industry says it needs to fill openings.

“There are just not enough visas,” said Tino Mantella, president and chief executive officer of the Technology Association of Georgia. “Right now in Georgia we know that there are over 4,000 job openings. We talk to companies every day that simply say they are struggling to fill jobs.”

Mantella and others said increasing the pool of workers either by hiring from overseas or making it easier for foreign students graduating with science and tech degrees to remain in the country is important if the state is to remain competitive. The $113 billion tech industry represents 17 percent of Georgia’s gross domestic product, TAG said.

Competition for the available 85,000 so-called H-1B visas is fierce. For the first time since 2008, the government may use a lottery to pick which companies are awarded the skilled-worker permits if requests exceed availability by Friday, as expected. The foreign workers must have at least a bachelor’s degree.

Metro Atlanta ranked No. 12 in the number of requests companies submitted for H-1B visas, with about 8,300 between 2010 and 2011, according to the U.S. Department of Labor. Those requests were among more than 325,000 nationally.

Many of the Georgia’s requests came from Georgia Tech and Emory University, according to the Brookings Institute. Others came from companies such as Deloitte Consulting Services, Manhattan Associates, GE Energy, Turner Broadcasting and Fiserv, which provides technology to the financial industry. The companies’ top needs were for skilled workers in computers, finance and engineering.

“It’s hard to get people who have the right background even if you are trying recruit out of state,” said Sam Lim, a director of operations for a unit of Cisco Systems in Lawrenceville. “Sometimes when you just run out of recruits your next best opportunity is to recruit outside the country, and to do that you need an H-1B.”

In the last two years the state has added 16,000 technology jobs, representing 20 percent of job growth during the period, TAG said. By 2018, Georgia will need 211,000 science and tech graduates, according to the Alliance for Science and Technology Research in America.

Georgia is one of the top states in science and technology graduates, mainly because of programs at Georgia Tech and Emory University.

Mantella, of TAG, said the state needs to have the ability to retain overseas students graduating with advanced degrees in computer sciences, engineering and other related disciplines to help fill job openings.

The organization also supports “rural sourcing,” finding talent in rural U.S. areas and providing training to help fill vacancies.

A portion of fees from companies’ H-1B visa requests is sent back to states in the form of grants for training Americans in science, technology, energy and math. According to the Department of Labor, metro Atlanta received about $16 million of more than $1 billion in visa fees for training from 2001 to 2011.