Illinois attorney general Tyrone C. Fahner estimates that his state loses $66 million a year in unemployment benefits paid to illegal aliens who use phony immigration documents when they apply for aid.

Similar cases involving welfare and food stamps were uncovered in California. Working with the Immigration and Naturalization Service, the state Department of Social Services sorted through a backlog of immigrant status forms last year, and found that hundreds of aliens in San Diego, Los Angeles and San Francisco had submitted fraudulent forms to qualify for benefits.

Fahner cited the Illinois cases last month at a Senate hearing on the use of counterfeit documents in federal benefit programs. Illegal aliens with papers that say they are permanent resident aliens, refugees or authorized for work can qualify for most benefits.

Estimating the magnitude of the problem is difficult, but some senators say aliens are defrauding the system of hundreds of millions of dollars and the government is doing little to stop them.

Despite the Reagan administration's stepped-up campaign to uncover fraud in federal benefits, a solution to the problem of forged immigration documents remains elusive.

INS officials say the agency doesn't have the money or the manpower itself to uncover forged documents. Part of the problem is that the agency's antiquated record system is still far from computerized. There is a nine-month delay, for instance, in providing new counterfeit-proof identity cards for legal immigrants.

Sen. William V. Roth Jr. (R-Del.), chairman of the Senate Governmental Affairs Committee, has asked Attorney General William French Smith and other administration officials to address the problem of document security. In the meantime, INS officials have called for an interagency task force to tackle the problem and are studying pilot programs around the country to see which uncover fraud most effectively.

The Illinois cases were discovered in one of those projects last spring when immigration officials were asked to check an applicant's eligibility for benefits by verifying the alien's identification or "green card."

In the first week, state workers found that 101 of 198 green cards presented at one Chicago unemployment office were fraudulent. Fahner said he was surprised that such verification wasn't routine in his or most other states.

A Fahner aide said recently that the discovery of fraudulent green cards among applicants for unemployment benefits has dropped to less than one in 10.

Federal officials are also concerned about the separate problem of fraud by legal aliens who come here temporarily as students. The estimated half-million foreign students who are here legally are not eligible for student aid or other benefits.

In Rhode Island and New York City recently, 34 foreign students were indicted for illegally receiving more than $200,000 in federal grants or loans to attend college.

Joseph F. Salgado, associate INS commissioner for enforcement, said, "This is the tip of the iceberg of something that's been going on for years. Because we're a nation of immigrants, there's been a philosophical hesitation to enforce the immigration laws. But now it's starting to hurt."

On the other hand, Arnold Torres, executive director of the League of United Latin American Citizens, said in a recent telephone interview, "The problem with some of these anti-fraud efforts is that it leads to harassment of legal residents. And it creates a mentality that constantly blames the undocumented for the problems of this country."

The eligibility and verification requirements of the main benefit programs vary widely and often can be bypassed, federal and state officials said at the subcommittee hearing.

A convicted forger told the subcommittee that he had great success counterfeiting packets of documents that included Social Security and INS "green cards." A subcommitee staff report added that arrival/departure forms for temporary visitors--called I-94s--can be stamped "refugee" or "work authorized" by forgers, entitling the bearer to full federal benefits.

INS' Salgado said the I-94 is subject to abuse because it is so widely available that even airline companies print up the forms. It never was intended to be an identification document for benefits, although it often is, he said.

He said he is sending a letter to executive branch inspectors general telling them I-94s shouldn't be permitted as identification for benefits.

Student aid fraud investigations of citizens and aliens are more difficult because applicants fill out forms for banks or state agencies without having to supply any identification at all, officials said.

Ray Scott, director of field investigations for the inspector general's office at the Department of Education, said a college official's suspicions about the number of African students applying for student aid was the first tip in breaking the Rhode Island fraud case. The names were then checked manually at INS.

James B. Thomas Jr., Education Department inspector general, said his staff is working with INS officials in all 10 regional offices to see how widespread such fraud is in the multi-billion student aid programs. "This is the year of the alien student," he said. "We found some cases so we're going to hit it as long as it's hot."