With an estimated 40,000 homes damaged by deadly flooding, Louisiana could be looking at its biggest housing crunch since the horrendous, aftermath of Hurricane Katrina a decade ago.

People now are staying in shelters, bunking with friends or relatives or sleeping in trailers on their front lawns. Others unable or unwilling to leave their homes are living amid mud and the ever-present risk of mold in the steamy August heat.

Many victims will need an extended place to stay while they rebuild. Countless others had no flood insurance and may lack the means to repair their homes.

“I got nowhere else to go,” said Thomas Lee, 56, who ekes out a living as a drywall hanger — a skill that will come in handy. His sodden furniture is piled curbside and the drywall in his rented house is puckering, but Thomas still plans to stay there, sleeping on an air mattress.

State officials are urging landlords to allow short-term leases and encouraging people to rent out any empty space available.

Terri Ricks, deputy secretary for the Department of Children and Family Services, which helps organize local sheltering efforts, said the state is talking with parishes about possibly running a long-term shelter to give people a place to stay while they repair and rebuild.

“Nobody wants to do a long-term shelter,” she said. “We want to get people in a more permanent situation.”

The Federal Emergency Management Agency, whose very name became a punchline during Katrina, said it will look into lining up rental properties for those left homeless and will consider using temporary housing units.

But FEMA Administrator Craig Fugate gave assurances that the temporary units won’t be the old FEMA travel trailers — a reference to the ones brought in after Hurricanes Katrina and Rita that were found to have toxic levels of formaldehyde.

FEMA aid has started flowing to people with damage, according to the governor’s office, which said nearly 1,400 houses have been inspected by the federal agency. About $900,000 has been paid to homeowners in FEMA individual assistance so far, of $7.6 million that has been approved for disbursement.