Ask CEOs and corporate recruiters whether they're finding the workers they need, and they'll lament about a skills gap that threatens productivity and growth–-not just in their companies but in the economy at large.

Yet employers and state legislators have been decidedly lukewarm about a proven solution to the problem: apprenticeships.

Apprenticeships can offer a precise match between the skills employers want and the training workers receive, says Robert Lerman, an economics professor at American University.

"It's a great model for transferring skills from one generation to the next," says John Ladd, director of the Department of Labor's Office of Apprenticeship.

Nevertheless, according to the Labor Department, formal programs that combine on-the-job learning with mentorships and classroom education fell 40% in the U.S. between 2003 and 2013.

All of which leads to the question: If apprenticeships are the solution to a pressing problem, why is there so much resistance?

Blue-Collar Image

Perhaps the biggest obstacle is that two-thirds of apprenticeship programs in the U.S. are in the construction industry, furthering a blue-collar image that stifles interest among young people and the employers who could create jobs for them. Construction unions, which dominate many of the state agencies devoted to apprenticeships, haven't done much outreach to other industries, Mr. Lerman says.

At the same time, business owners and managers sometimes shy away from apprenticeships because of their association with unions. "There's an underlying fear among employers" that unions want to come in and organize workers, or that any apprenticeship program would be run by a union, says J. Ronald DeJuliis, head of labor and industry at Maryland's Department of Labor.

Yet, he and others say, it doesn't have to be that way. Apprenticeships today involve lots more industries than the handful of trades that embraced the earn-and-learn model beginning in 1937 when the National Apprenticeship Act was passed. Nursing assistants, wastewater technicians and computer-system administrators are among the positions for which apprentices can now train.

Earlier this month, President Obama set aside $100 million to go toward apprenticeships in high-growth industries, and recognized new programs in health care, information technology and supply-chain management.

Another damper is a widely held view that young people should stay in school and then get a job. Advocates of apprenticeships say this thinking is misguided.

College degrees and internships don't produce the same quality of worker as intensive, on-the-job apprenticeships, says Brad Neese, director of Apprenticeship Carolina, a program of the South Carolina Technical College System. Employers are seeing "a real lack of applicability in terms of skill level" from college graduates, Mr. Neese says. "Interns do grunt work, generally." In contrast, he says, "an apprenticeship is a real job."

Some companies also fear that employees will leave for better-paying jobs almost as soon as they've learned their required skills. For them, an apprenticeship amounts to training workers for other companies.

But in many cases, employers are finding that apprenticeships actually help with retention, as workers who come up through apprenticeships see the investment their employers are making in their career and reciprocate with a greater sense of loyalty.

"The apprenticeship model helps us show people there's a career path within this company," says Robby Hill, owner of HillSouth, a Florence, S.C., technology consulting firm taking advantage of South Carolina's on-the-job training program. New employees see the opportunities ahead, along with a clearly delineated ladder of skill acquisition and salary increases, says Mr. Hill, whose 22-person firm offers apprenticeships for IT and administrative-support employees. The company also asks employees to sign noncompete agreements as they get accredited for new skills.

Innovative Thinking

Proponents of apprenticeships argue that blending on-the-job training, related education and benchmarks can be done in any occupation. They point to programs in places like South Carolina and Wisconsin as producing encouraging results.

Apprenticeships now exist for computer professionals and for certified nursing assistants in South Carolina, where the number of businesses offering apprenticeships has grown to 647 from 90 in 2007. Some 4,700 people who trained in South Carolina's apprentice program are now fully employed.

To get employers involved, the state offers a $1,000 annual tax credit for each apprentice on the payroll. "That helps open the door," says Mr. Neese. "For a small business, the credit can wipe out the education costs for an apprentice program.

"We've tried to make the tax credit as user-friendly as possible," he adds. "We have a very simple one-page form that literally says, 'How many apprentices do you have?' and then you multiple that number by $1,000."

Wisconsin, which has about 8,000 apprentices currently, is pushing to add training positions for skills from truck driving to high-tech manufacturing.

"We're projecting worker shortages in health care and advanced manufacturing," says Karen Morgan, director of Wisconsin's Bureau of Apprenticeship Standards. The Governor's Council on Workforce Investment is looking at what it can do, she says. The state has several programs to add robotics and high-level welding to its regular apprenticeship training.

"We're making our programs more nimble," Ms. Morgan says, to show manufacturers the relevance apprenticeships can have for a sector undergoing rapid innovation.