BEAUMONT, Texas (AP) — His three vehicles flooded by Hurricane Harvey, Jason Bell checked at one car-rental office only to find about 2,500 people ahead of him on the waiting list. When he tried a more out-of-the-way location, the reservations still numbered about 300.

Many other storm victims have the same problem. Tens of thousands of personal vehicles were inundated by floodwaters or smashed by wind-tossed objects, creating a huge demand for rentals that has put the cars in painfully short supply in the Houston area and across eastern Texas.

Rental companies say they are bringing in more ve...