State Police Capt. Dave Bursten said it's now taking 15 weeks to get one permit request processed, a time that's nearly doubled the average wait time.
"When we had our traditional number in a normal year, we were running in the area of eight or nine weeks if you had a traditional fingerprinting, a little under five weeks if it's an electronic fingerprint," he said.
Local police departments, meanwhile, are getting bogged down with inspections, fingerprinting and background checks needed for each permit application.
Each application must be reviewed and either approved or rejected by the local police chief, town marshal or county sheriff. State Police have the final decision on approving and issuing the permits.
Carmel Police Chief Tim Green said the suburban Indianapolis city of 80,000 had 263 new applications filed in the first five weeks of 2013, compared with 67 applications in the same period last year. Green said Carmel could surpass 1,000 new permits this year, nearly 200 more than in any previous year.
"Many of these folks want the permit because they are afraid they will not have the ability to get one in the future," Green said.
In Indianapolis, the city's police department received more than 1,100 applications in December. That's 360 more than the department received in November.
But the increase in requests seems especially pronounced in the suburban and rural areas surrounding Indianapolis.
Greenwood police spokesman Matt Fillenwarth said the department just south of Indianapolis processed 196 permits from November to January, compared with 47 during the same time a year earlier.
The increase follows the national debate over gun violence and new gun restrictions that began after a 20-year-old gunman fatally shot and killed 20 children and six adult staff members Dec. 14 at Sandy Hook Elementary School in Newtown, Conn.
"Ever since the president started talking about gun control after the Sandy Hook shooting, I mean we've seen a tenfold increase in the people that have come in wanting to get gun permits," Fillenwarth said. "I think it's been slowing down a little bit, but any time they talk about any type of gun control, people freak out."
Law enforcement officials said the increase in permit applications illustrates the confusion over Indiana's existing guns laws because most of the people seeking the gun permits don't need them.
That's because Indiana residents don't need to have a permit of any kind to own or use a rifle or shotgun, or to own or keep a handgun in one's home.
However, a permit is needed if gun owners intend to carry a handgun on their person or in their vehicle.
Indianapolis resident Steven Cutler, 58, recently sought a permit because he wants to carry his gun in his vehicle to shoot targets. He said he's motivated by concerns about potential restrictions but also is concerned about his personal safety in case he encounters unexpected dangers.
"With the upcoming potential regulations and tightening of the laws, I thought it would be a good idea to get some self-protection," Cutler said.