Old Town Alexandria is beginning to discover one of the inevitable problems of urban success - a shortage of parking spaces.

Small lots that used to provide parking for one or two dozen cars have given way to rows of $160,000 townhouses. Buildings formerly occupied by low-income families with no automobiles are being renovated and sold to wealthier people who own one or more cars. A profusion of restaurants and shops attracts a growing number of visitors who must frequently cruise the streets before they can find a parking space.

City officials have estimated that the Old Town parking supply, adequate for demand as recently as 1975, will fall 1,000 spaces short of satisfying demand every weekday of this year and next.

The problem is not as severe as it is in Georgetown on a weekend night or in downtown Washington on a work day, but the parking situation has deteriorated enough during the past months so that merchants in the area believe something must be done soon or business may suffer.

"Unless we do something about the parking we're going to head-off the success Old Town has had," said Gus Pikrallidas, owner of the John Bull restaurant across from the Alexandria City Hall on N. Royal Street. Pikrallidas explained that he recently lost a luncheon that had been planned for 18 persons because of the parking problem.

Although the parking problem has been growing for some time, it became severe when construction started on a new $10 million courthouse and commercial structure on the 500 block of King Street in the heart of Alexandria's commercial corridor. The start of construction last month meant the immediate loss of 195 parking spaces.

"Right now we wouldn't be feeling this crunch at all if it weren't for the construction of the courthouse," remarked Robert E. Bellavance, the executive vice president of the Alexandria Chamber of Commerce.

"The parking problem," Bellavance continued, "has slowed down growth. We're going to have a couple of tight years here. We're going to hurt a bit, but I can see ourselves pulling out of it."

Merchants in Old Town say that the immediate need is to provide for additional parking spaces in the downtown area, now generally described as extending from Rte. 1 to the Potomac River. Residents in Old Town, however, appear to favor setting up a residential parking permit system which would limit parking for non-residents of the area to two hours.

"You have the most problems on weekends when there are more people visiting Old Town," said retired Air Force Col. Drew T. St. John, who lives in the 100 block of Cameron Street. St. John said that until a few years ago residents had no problem parking near their homes, but that today those spaces are frequently taken by employes in the nearby restaurants and shops as well as by City Hall personnel.

A residential parking permit system would in effect transfer the parking supply from employes to shoppers," according to Clifford Rusch, Alexandria deputy city manager. Rusch estimates that 50 per cent of all employes in the downtown area live outside Alexandria and that many of these drive to work.

Alexandria officials have drawn up a proposed law that would regulate residential parking. A public hearing on the issue has been scheduled by the City Council on May 13. But Charles E. Kenyon, deputy director for transportation in Alexandria, warned: "The first thing we want you to know is what it will not do is guarantee you a reserved parking space in front of your house."

Other suggestions that are being considered by Alexandria officials would:

Insure greater turnover of parked cars by setting up more meters in the downtown area. The city is now adding 87 new meters in the area, 46 of them on five residential blocks.

Set up fringe parking areas just outside the business district and shuttle people back and forth on small buses. One of the areas suggested is the parking lot at Jones Point at the southern end of the Alexandria waterfront.

Encourage car pools. The Alexandria Chamber of Commerce is asking employes to fill out forms that will be run through the computer of the Metropolitan Council of Governments in order to identify potential car poolers.

Construct a ramp to the second floor of the "Doughnut Building" in the torpedo factory complex so the space can be used for parking. Currently about 150 cars park daily in the building's first floor.

The Old Town Business Association has said it will pay the $30,000 construction costs if its members get first priority for the additional spaces. Alexandria officials appear reluctant to take this approach because the future of the entire torpedo factory is in doubt.

Several City Council members lean towards demotion of the buildings to make room for a waterfront park.

Construct a multi-level, 400 car garage at Cameron and Columbus Streets. Edward Holland, chairman of the board of Park and Shop, which runs two garages in the city, says his company would be willing to build the structure, but may have to join with others to finance the project.

Holland said his group has raised monthly parking fees from $25 to $40 in the past 18 months to try to provide more spaces for shoppers and visitors by making the spaces costly for workers. Other lots in Alexandria have also increased their monthly and in some cases daily rates recently.