Mildred DiCosola and her family found out the hard way that tourists can't park at the Smithsonian museums on the Mall.

"We came early thinking we could park right down here," DiCosola said last week outside the National Air and Space Museum, which has a 495-space underground parking garage. The Long Island family wound up parking at Union Station and walking about a mile.

"I think the garage should be for tourists instead of having us park so far away," DiCosola said.

Smithsonian officials closed the Air and Space garage, and public parking lots at the Natural History and American History museums, in 1986 because of fear that terrorists might drive into the parking areas and detonate bombs.

Although the terrorism fear mostly has disappeared, the 785 parking spaces at the Mall's three most popular museums have remained off-limits to the public. Meanwhile, senior employees of the Smithsonian have been allowed to park there for free.

"It's always irritated me that they didn't reopen the garage to the general public because it's always hard to get a space down here unless you get here early," said William Luken, of Alexandria, who took his out-of-town guests by Metro to the Air and Space Museum last week.

Though Smithsonian officials said they never promised to reopen the lots to visitors, they said they have considered allowing people to park there again. But spokeswoman Linda St. Thomas said Smithsonian Secretary Robert McC. Adams "does not see any reason to reverse" the 1986 decision.

"We'd like to think we offer many things, but parking isn't one of them," St. Thomas said. "We're in the middle of a downtown area. Would you try to drive to the Met in New York?"

The problem now, officials said, is not terrorism but a shortage of space for employees and equipment.

Six years ago, the Natural History Museum had 347 parking spaces in the outside lots east and west of the building at 10th Street and Constitution Avenue NW. Now there are 170 spaces because workers are installing new heating and cooling systems for the museum in the east lot. An average of 26,000 people a day visited the museum last month.

When the underground garage at the Air and Space Museum, at Seventh Street and Independence Avenue NW, was closed, it had 511 parking spaces. Now, because of construction of offices in the garage, there are 495 spaces. The American History Museum lot had 124 spaces in 1986, compared with 120 spaces now. The museum is at 12th Street and Constitution Avenue NW.

Even if the parking garage and lots were opened again, Smithsonian officials said, there would not be enough spaces for everyone who wanted them. Nearly 20 million people visited the three museums last year; the Air and Space Museum is the nation's busiest.

"We're not talking Tysons Corner here," St. Thomas said, referring to the acres of parking at the area's largest shopping center, located in Northern Virginia. "We encourage people not to drive to the Smithsonian."

The message has been heard.

Martha Bryant, of Hot Springs, Ark., whose family rode Metro to the Air and Space Museum, said: "My husband was quite upset because he likes to have the car. But as soon as we got into town, everyone said, 'Don't drive anywhere. Take Metro.' "

Although Smithsonian officials encourage visitors to take Metro, their free-parking policy likely discourages some employees from using the subway.

Free parking for government and private employees is a reason that Metro officials say they have trouble attracting new riders. Workers who do not pay for parking have little incentive to ride mass transit, officials say.

Not charging employees for parking also has cost the Smithsonian tens of thousands of dollars a year at a time when it is laying off employees and cutting other costs to make up an estimated $40 million budget shortfall. Visitors had paid an average of $5.25 a day to park at the museums.

The free parking may be about to end, however. In a recent memo sent to the Smithsonian's 6,600 employees, officials said a task force will recommend a new policy that could include charging workers for parking beginning Oct. 1.

St. Thomas said that if an end to free parking is recommended, the rationale would be to stimulate transit use and bring in new revenue for the Smithsonian.

Mark Turner, of Woodbridge, N.J., said he would be happy to pay for parking if officials would reopen the garage under the Air and Space Museum. With his wife and four sons in tow, Turner drove around the Mall area for about 40 minutes one recent morning before finding a metered parking space on the street, he said.

"It would be so much more convenient parking at the museum," he began. "Oh, excuse me. I've got to go feed the meter."