The holding lot for B and P Towing on Shirlington Road in Arlington was so full at one point this week that workers had trouble swinging open the gate. And nearby, a police department tow lot meant to hold 280 cars held about 400.

Unable to dispose of vehicles as fast as they're pulled off the streets, Arlington is awash in towed cars. But some county officials think they've found the solution: Tow the cars outside the county.

Encouraged by local officials, Del. Mary Marshall and state Sen. Edward Holland, Democrats who represent Arlington in the General Assembly, sponsored a bill exempting the county from a state law that requires that cars towed for outstanding parking tickets be stored in the city or county that issued the tickets. Cars towed under other circumstances can already be towed to approved lots outside Arlington.

In Richmond, the legislation sailed through the Senate, but ran into a snag in the House of Delegates, where Del. Arthur R. (Pete) Giesen Jr. (R-Waynesboro) worried that "an affluent county like Arlington might decide to tow a car to Wise County," 400 miles away in far Southwest.

After Marshall agreed to an amendment that restricts the towing to an adjoining city or county, the bill was passed, and now awaits the signature of Gov. Gerald L. Baliles.

The change in the law will give the county greater flexibility in dealing with the crowding in tow lots and might prove cheaper to car owners if the county is able to lease inexpensive lots in neighboring jurisdictions, said Sgt. Gary W. Gossett, who oversees police towing operations.

Car owners are now charged $15 a day storage fees on top of towing fees of $45 to $65.

The proposal has met with less than enthusiastic response from Arlington's neighbors.

"There's no place to store cars over here," said Fairfax County Supervisor Thomas M. Davis III, whose district adjoins Arlington.

Land costs are just as expensive in Fairfax and a new storage lot would require a zoning variance "from yours truly," and "it isn't available," said Davis.

Actually, fewer cars were towed in Arlington last year than the year before: 4,940 in 1987 as opposed to 5,622 in 1986. But crowding has resulted because owners now tend to leave their cars in the lots longer and because land for new lots or expansion of old ones has grown increasingly scarce and costly in the rapidly urbanizing county, according to police and tow company officials.

"Storage lots are being taken over by development," said Deputy Police Chief Robert A. Dreischer. "Land is at a premium."

"There is no space available {in the county} that can be bought or leased that is zoned for the storage of cars," said Frank R. Simino, office manager for B and P Towing, which has an exclusive contract with the police department to tow cars.

Residents are often reluctant to have a storage lot in their neighborhood because "it doesn't look good to have a junkyard, which is what it looks like," he said. In addition to its Shirlington lot, the firm has a storage lot in Crystal City.

He agrees that poor turnover has also contributed to the crowding problem. A decade ago a car involved in an accident might sit in the lot for five days while insurance claims were settled and the car was picked up, said Simino. Now the wait might be 15 to 20 days, he said.

Abandoned cars are another problem. "If you have a 1971 car and $600 worth of parking tickets, it's not worth it to get the car," Simino said, adding that the transiency of Arlington's population contributes to the number of abandoned vehicles.

The county in 1986 passed an ordinance aimed at getting junked or abandoned cars off Arlington streets. Abandoned vehicles deemed inoperable are taken to a junkyard after attempts to contact owners.

Operable vehicles that appear to be abandoned are towed. It takes up to 45 days to contact owners and determine whether those cars can be scrapped, said Gossett of the police department. This contributes to the backlog in the storage yards.

"We just can't keep up with it," he said.