It’s never been easy — and it may be getting harder — to find an unemployed computer-science major in Washington state.

Just ask Steve Singh, the CEO of a company with 700 job openings worldwide — 300 of them in Washington.

“We have a standing discussion with University of Washington computer science — anybody you graduate, we’ll take,” said Singh, CEO of Redmond-based Concur Technologies.

The shortage has been an ongoing issue in Washington, but as the state emerges from the economic downturn, pressure is building to grow college programs that could fill the gap.

This week, the business group Washington Roundtable released a study that says 25,000 high-skill jobs in Washington are going unfilled — jobs that have remained vacant for three months or longer, because qualified workers can’t be found to fill them.

An additional 5,000 high-tech jobs in computer science, engineering and health care are forecast to open up each year for the foreseeable future.

Those high-paying jobs themselves create more jobs, as employees buy houses and cars, and spend money in other ways that stimulate the economy. The Washington Roundtable believes that filling those jobs could create an additional 110,000 “multiplier” jobs and boost annual sales-tax collections by $720 million.

The study comes at a time when state legislators are busy writing budget proposals for the biennium, mindful of a $1 billion budget deficit and the need to boost funding of K-12 education.

“We’ve demonstrated that if you invest in higher education, there’s a clear return on investment,” said Steve Mullin, Washington Roundtable president. “When you try to think how we should invest our scarce economic-development resources, we’re suggesting this should be the priority.”

The Roundtable, made up of CEOs from the region’s largest companies, is not putting a dollar figure on the cost of high-tech training, and does not propose a way to pay for it.

During the downturn, Washington made some of the sharpest cuts in higher education in the nation.

An analysis by Illinois State University’s Center for the Study of Education Policy shows that Washington’s support for higher education, which includes financial aid, has been cut by 22 percent in the past five years. The national average is 11 percent. Only seven states cut higher education more severely than Washington.

The cuts have prevented Washington’s universities from significantly expanding computer science and engineering, even though demand has soared.

At the University of Washington last year, more than 1,600 students applied for slots in the College of Engineering. The school could admit only about 800.

The crunch was particularly acute in the Department of Computer Science and Engineering, where 165 upper-division students were admitted to the department from a pool of 639 applicants.

The Roundtable study calls for more science, technology, engineering and math (STEM) education in K-12. It also calls for a better alignment in community colleges of technical degrees and certificate curricula with employer demands.

But Marty Brown, executive director of the State Board for Community and Technical Colleges, said the colleges have tried to respond to industry needs, and that industry leaders need to give more specific information about what they want.

For example, the colleges have increased training for machinists and welders at Boeing’s request, aided by a $16 million appropriation from the state for training equipment, Brown said.

Yet last week, Boeing announced it would lay off 800 to 1,000 machinists. “I don’t know what’s going on,” Brown said.

Nicole Smith, a senior economist at Georgetown University’s Center on Education and the Workforce, said the Roundtable’s figure of 25,000 unfilled jobs in Washington sounded right.

She helped write a 2010 Georgetown study predicting that by 2018, 67 percent of the jobs in Washington will require postsecondary education.

Smith said the high wages that entry-level engineers and computer analysts are making buttresses the argument that there’s a need for more degrees in science, technology, engineering and math.

“These are some of the highest-paid entry-level jobs in the country,” she said. “The market is telling you there’s excess demand compared to supply, or employers wouldn’t be paying a premium.”

Katherine Long: 206-464-2219 or klong@seattletimes.com.

On Twitter @katherinelong.