NEW YORK -- Thanksgiving travelers who have yet to rent a car in the Northeast are out of luck: Superstorm Sandy has created a shortage.

The storm has damaged thousands of cars – including those owned by rental companies. The loss of vehicles has been compounded by rising demand. Thanksgiving and Christmas are normally busy rental periods. And lingering mass transit problems caused by Sandy have added to demand.

Existing reservations are mostly being honored, but people who still want to book for Thanksgiving are finding almost no cars left. The few cars available carry a hefty premium.

Tadd Rosenfeld is flying into New York’s LaGuardia airport Wednesday. He couldn’t find a car with any major rental company. U-Save was the only one with a car and it wanted nearly $350 a day – more than his plane ticket from Miami. Now, he is considering renting a moving truck.

“Showing up to Thanksgiving in a U-Haul is worse than showing up with an escort. But at $19 a day, it’s tempting,” says Rosenfeld, CEO of TeamLauncher.com, a Miami-based outsourcing company.

To help ease the shortage, car rental companies have driven in thousands of extra vehicles from elsewhere in the country. They have also kept older models that they would normally sell to used-car dealers.

They’ll need every car. Thousands of people in the Northeast are still without vehicles. Some cars were flooded by surging waters and will be replaced with new ones once insurance checks are cut. Others were damaged by falling trees and debris and are in body shops waiting to be repaired

Insurance companies State Farm, Progressive, New Jersey Manufacturers, Nationwide and USAA told The Associated Press in the days following the storm that they received about 38,000 car-damage claims. Other companies either did not return calls or declined to release claims information.

“It’s an unusual situation,” says Neil Abrams of the Abrams Consulting Group, which focuses on the car rental industry. “Unfortunately, you can’t go out and buy cars for a demand spike. You don’t know how long it will last.”

Car rental companies were hesitant to speak about their own losses but Avis Budget Group Inc. says it removed from service 2 percent of its fleet from Philadelphia to Connecticut. The company did not respond to repeated requests to clarify how many cars that was.

Outside of the holiday rush, car rental companies say there are enough vehicles available for drivers. Here’s what they did to ensure a large enough fleet:

•  Hertz held on to older vehicles that were scheduled to be sold. It also brought in extra cars and even rented trailers and generators to keep open some locations destroyed by the storm.

•  Avis Budget brought in 6,000 extra cars from elsewhere in the country.

•  Enterprise Holdings – which owns Enterprise Rent-A-Car, National Car Rental and Alamo Rent A Car – moved 17,000 cars to the Northeast region from other parts of the country. Another 10,000 brand new cars, slated for other states, were instead redirected to New York and New Jersey.