Hurricane Harvey may inflict as much as $30 billion in damages on homeowners, according to preliminary estimates. But only 40 percent of that total may be covered by insurance — and of that, the federal government will bear the biggest liability.

Private homeowners’ policies generally cover wind damage and, in certain cases, water damage from storm surges. But for almost half a century, all other homeowners’ flood coverage has been underwritten by the National Flood Insurance Program, a federal program that itself faces financial uncertainty.

Flooding has dealt the hurricane’s biggest blow. And in areas where it is prudent — or even obligatory — to buy it, having flood coverage is the exception rather than the norm.

Homeowners in areas designated as 100-year flood zones are required to hold policies from the federal program. But in practice, the requirement is difficult to enforce and most people — including in eastern Texas — fail to buy coverage or let their policies lapse by not keeping up on the premiums.

“It’s a pretty cheap buy,” said Charles C. Watson Jr., a founder of Enki Holdings L.L.C., a data analytics firm for natural disasters, who offered the $30 billion estimate for the overall damage to homes. (CoreLogic, a firm that analyzes real estate and insurance data, estimated that private insurance would wind up covering from $1.5 billion to $3 billion.)

Mr. Watson, who lives in what he believes to be a flood-prone area of South Carolina, said only he and a couple of his neighbors had flood coverage, even though the premiums are far lower than the cost of potential claims.

The Federal Emergency Management Agency issues maps showing 100-year floodplains, and bases flood insurance rates on those. The maps provide good data on where storm surges may hit, or rivers may overflow their banks, said Carolyn Kousky, director of policy research at the Wharton School’s Risk Management and Decision Processes Center.

“But what they don’t handle well is when a downpour overwhelms a local storm-water drainage system,” she said. That is what is now happening in the Houston area, “on a scale that’s never been seen before,” she said.

That means many homeowners with water now up to their knees, or higher, were never required to buy flood insurance, because their property was not listed as being on a 100-year floodplain.

Harris County, which includes Houston, started using new floodplain maps from FEMA in January. The maps added about 8,000 parcels to the agency’s Special Flood Hazard Areas, meaning those properties have a better than a one-in-four chance of flooding at some point during a 30-year mortgage.

Local authorities in Houston worked with FEMA to get the word out about the need for flood insurance, but it was a hard sell. And now that there is a flood, it is too late to buy it.

People without coverage will have to apply for grants or low-cost loans from other branches of the federal government, said Loretta Worters, a spokeswoman for the Insurance Information Institute. That means delays in receiving funds, if such requests are even approved.

A FEMA spokeswoman said the agency would have National Flood Insurance Program claims statistics for Harvey later this week.

The National Flood Insurance Program was created in 1968, after most private insurance companies stopped writing homeowners’ flood coverage because they could not charge premiums high enough to cover the potentially catastrophic costs. (In addition to wind and limited storm-surge damage, private insurers cover vehicles caught in flooding.)

The 49-year-old program is now run by FEMA. Its coverage has caps: $250,000 for a house and $100,000 for its contents, and $500,000 apiece for a business building and its contents. Larger companies can still buy flood coverage through commercial insurers.