Denise Dickerson was delivering 20 bales of hay and a carnival game to a company picnic earlier this month when the 1968 truck she was driving broke down on I-95, south of Alexandria. Several hours later, Dickerson's father, Duane, received a call from Virginia State Police telling him that the unattended truck had been a traffic hazard and had been towed to a nearby storage lot.

It cost Dickerson $105 to recover his truck from Franconia Towing, one of about 25 private Northern Virginia towing companies used by state police to clear unattended cars off highway shoulders.

The number of cars towed off Virginia highways has doubled in the last six months, the result of intensified efforts by state police. In 1984, state officials reported that 3,744 unattended cars were towed from its highways, which includes portions of I-66, I-95, I-395 and I-495. In just the first six months of 1985, there were 3,273 abandoned cars were towed to privately owned storage lots.

Capt. Herbert D. Northern, who directs the state police's towing program in this area, said nine additional troopers were added to the I-66 corridor and seven more patrols were added to the new Dulles Toll Road.

Northern blames the sharp increase in towing on improper car maintenance and to motorists' unawareness of the state's law against leaving cars unattended on interstate highways. The state highway department has installed 15 huge rectangular signs along the 92 miles of Northern Virginia's interstates to warn drivers about the 20-year-old law and its expensive consequences.

Northern labels the unattended cars "traffic hazards. From 1978 to 1983, unattended vehicles have accounted for 524 accidents, 275 injuries, 20 deaths and property damage in excess of $1.5 million," he said.

Northern said a driver can leave a car unattended for 24 hours, and only if it is parked on the grassy portion of the highway. He said the highway shoulders must remain clear to allow emergency vehicles access to accidents.

Northern said it could cost as much as $112 to recover a car from a towing company storage lot. He said towing and storage fees vary among companies. Companies tow abandoned vehicles only after they have been notified by state police.

Bruce L. Hecox, president of Hecox Inc., which owns Franconia Towing, said he has about 150 cars in his storage lot on Vine Street, the majority of them left unattended on the highway.

Hecox, who runs his operation for the state police 24 hours a day, charges a driver $45 to tow a car off the highway and $10 a day in storage fees. There is an additional $25 charge for more complicated towing work.

Jim Kinsella, manager of Beltway Mobil on Rte. 236, said that last week he received between 10 and 12 calls from the state police to tow unattended cars from the highway.

"There's been an increase in business, without a doubt," Kinsella said.

Kinsella charges $45 to tow standard-sized cars and $55 to tow sportier models, such as Porsches, Corvettes or Jaguars. There is an extra $10 charge to unlock a car's transmission and another charge ("between $35 and $150") to tow the car from an embankment.

Northern said motorists should stay with their cars and wait for assistance instead of leaving to look for help. He said if drivers abandon their cars but leave an explanatory note on the windshield, a state trooper will usually allow enough time for the person to make arrangements and get back to the car.

But Dickerson, who also lost $350 in business the day his truck was towed, said the state police should give drivers more time to return to their cars. "I don't see why they don't give you until the next business day to get the car," he said.