When their modest house in rural Virginia burned down last April, the owners called their agent for State Farm Fire & Casualty Co. and filed a claim on their homeowners' policy. They estimated their loss at $43,500.

Later the same day, they called another agent, representing Nationwide Insurance Co., and filed another claim, putting the loss at $45,000.

Neither insurance company knew about the other's policy, nor did the Virginia state police, who investigated the fire, know that the owners had double coverage. But they discovered the dual policies, and a possible motive for arson, within a few days when both insurance companies fed routine reports of the claims into a computer here.

The computer contains the Property Insurance Loss Register, known in the insurance business as Pillar, a new and apparently potent weapon in the insurance industry's frustrating battle against arson for profit.

Virtually every fire damage claim over $1,000 filed with 720 insurance companies who write more than 90 percent of the nation's $19 billion in annual fire insurance premiums is now reported to Pillar. All details of each incident are recorded--owner, owner's partners, tenant, location, mortgage holder, adjuster--and the computer runs 466 combinations of cross checks on every claim.

The result, according to Pillar director Gerald F. Murphy, is more than 900 "hits" a month, incidents in which the computer turns up multiple coverage, previous claims by the same person or on the same site, or some other reason for claims adjusters--and the police--to look twice at the circumstances of the fire.

"We get basic information, 'just the facts,' as Joe Friday used to say," Murphy said. "Our report to the adjusters tells what it was that flagged this claim. It does not say anyone is an arsonist."

Nevertheless, it is "going to be invaluable" to insurance companies, said John Barracato, director of the arson and fraud unit of Aetna Casualty & Surety Co., one of the largest companies. "To deny a claim, we have to show arson was committed, we have to show motive and opportunity. When we get a hit, it starts to establish the motive. This will uncover the repeaters as well."

Arson is one of the major causes of property damage in the United States. Though statistics are erratic because of differing reporting methods, the U.S. Fire Administration has calculated that in 1980 about 670,000 of the 33 million fires in the nation were "incendiary or suspicious." They caused 1,094 deaths and damage estimated at $1.7 billion.

Studies by the federal Law Enforcement Assistance Administration and the insurance industry indicate that profit or fraud is the motivation for only about 14 percent of arson fires (vandalism and spite or revenge account for 65 percent), but these cause about 40 percent of the total damage. The kind of warehouse fire arranged by Jack Lemmon in the movie "Save the Tiger" is far more costly than the grass fire set by teen-agers, insurance experts point out.

According to Murphy and other property-loss insurance specialists, economic hard times generally lead to an increase in financially motivated arson: hard-pressed business executives arrange for the torching of warehouses full of unsold merchandise, farmers burn down barns to collect the insurance money, homeowners store their valuables with a relative and report them stolen, apartment house owners make phony sales to increase the reported value and burn the buildings down to collect the higher insurance coverage.

"In 1974, people torched their gas-guzzler cars," Murphy said.

The establishment of Pillar less than two years ago gave the insurance companies a way to spot possible clues to fraud and multiple claims, which could enable them to reduce payouts and premiums. Only New York State has made participation mandatory, but all the major companies and most of the smaller ones in every state have signed up and agreed to pay their share of the cost, Murphy said.

G. Patrick Riggs, senior vice president for claims services of the American Insurance Association, the trade group sponsoring Pillar, said it is "informational only, a tool for evaluating claims. The local insurance company must make its own decision about what to do with the information."

Even if no criminal case is developed by fire investigators, he said, "you can still make a civil case by denying the claim and putting the burden on the claimant."

Riggs and Murphy said Pillar information is never used to evaluate an applicant for insurance coverage, only to check on claims after they are filed. But information developed through the Pillar reporting system may be turned over to police or fire investigators, they said.

The American Insurance Association says 48 states, including Maryland and Virginia, have enacted laws shielding insurance companies from suit for libel when they turn over information about suspicious fires to the police. Many of those laws actually require the reporting of suspicious incidents, in the same way as many state laws require hospital personnel to report suspected child abuse to authorities. The result, they said, is that the insurance companies are now free to work with police and fire marshals in tracking down possible arsonists.

Murphy, who joined Pillar after a long career as a fire claims adjuster--"there isn't anything that won't burn, but the worst is a fire in a chicken coop"--said that many claims flagged by the Pillar computer do not indicate arson.

He cited the example of a man in Richmond who has filed seven claims since early 1980. The man owns several residential properties in a low-income, high-crime area, the reports show, and the fires have been attributed to such common causes as cigarettes burning in bedding, children playing with a kerosene heater, and fire in the adjacent building. In the case of the rural Virginia house fire where a double claim was filed, state police investigators ruled the fire was accidental. They said the homeowner apparently was changing from one company to another at the time and filed both claims to make sure he was covered.

Arson by itself is not sufficient grounds for an insurance company to reject a claim, Murphy and Riggs said. If there is no indication that the claimant was responsible, they said, he or she is entitled to collect. But when a man in Pennsylvania filed $20,000 claims with five different companies on a $30,000 house, they said, all refused to pay the full amount.

Murphy is also the custodian of an archive of theft and burglary loss claims. This works much the same way as Pillar, flagging such offenders as a New Jersey couple who claimed the same luggage theft four times, but it is not computerized. It consists of more than 2 million index cards, filled out and entered by hand.

Before the end of this year, Murphy said, those records will be computerized and combined with the fire records, to create one comprehensive roster of claims for fire, theft and burglary. "People running insurance frauds don't usually limit themselves to one type," he said.