The new federal-state "runaway fathers" program has helped the states rake in $1.6 billion over the past two years by tracing absent fathers and making them support their children - at a cost of $457 million to the federal, state and local governments.

While some fathers are too poor to pay, the program's deputy director, Louis B. Hays, said in an interview that officials have discovered plenty of well-to-do fathers:

In Sacramento, officials in one nonsupport action discovered the father was a retired military officer who was collecting both, a pension and a total income of $60,000 a year.

In Michigan, a law student who had divorced his wife years earlier and fallen $5,000 behind on $20-a-month child-support payments was tracked down when his family went on welfare. He had advanced considerably in his profession - he was now a judge.

Also in Michigan, a man who at the time of his divorce was ordered to pay $100-a-month-child support, was $13,000 in arrears. His family went on welfare. He was tracked down and discovered to be an official of an aircraft manufacturing company in California. When he learned that officials were after him, he turned the matter over to his attorney and sent $10,000 as a downpayment on his arrears. "He's now caught up and current in his payments," said Hays.

In Utah, a man in default on monthly payments was found to own half a financial corporation and a fast-food chain. "He's now paying $625 a month and is current in his payments," said Hays.

Hays said that while statistics are still not complete, at least half of the fathers tracked down "have the capacity to pay some reasonable level of child support and some have rather substantial incomes."

"State officials say some doctors and lawyers making up to $100,000 a year have been evading child support. Not a high percent, but a few hundred."

Some states are reaping big dividends. California collected $141 million last year, Pennsylvania $156 million.(Maryland collected $7.5 million, Virginia $5.4 million and the District of Columbia $600,000.)

Four years ago, when Russell B. Long (D-La.) pushed through a Senate amendment creating a federal program to track down runaway fathers of welfare children, there was lots of sniggering and huffing from Long's critics.

One of the nation's leading social welfare experts said in the corridor outside the Senate Finance Committee, "What's the point? Most of these men have no money to collect anyway."

The Washington Post editorialized, "An unwarranted intrusion of the federal government [into personal lives] . . . would yield little while costing a great deal . . . the benefits to be derived are minimal at best. The dangers are incalculable."

Today, no one is sniggering. About 1 million parents who otherwise would pay nothing are now making payments. The program is now running at a rate of over $1 billion a year in child-support payments obtained for welfare mothers or other families where the father has disappeared or refused to support the children. That figure is equal to about 10 percent of the entire national cost of the program of Aid to Families with Dependent Children.

"This program is a success," said Secretary of Health, Education and Welfare Joseph A. Califano Jr., warmly praising Long for his efforts to get it enacted in 1974.

Before the program was passed, a mother who wanted child support from the father of her children had to go to court or the state welfare agency and try to (1) establish paternity if it were in doubt; (2) seek to obtain an order requiring payment of child support by the father.

It cost money to hire a lawyer, it was complicated to do, and for low-education welfare mothers without any money it was often impossible.

A few states had agencies to take over the responsibility, but there wasn't any systematic nationwide program.

The Long amendment changed all that. First, it required every state, as a condition of receiving federal welfare subsidies under the AFDC program, to set up a separate unit specifically charged with conducting an active program to track down "fleeing fathers."

Second, it specified that the state give such assistance not only to welfare mothers, but to any parent with children where the other parent was absent and not participating in the children's support.

Third, it provided for the federal government to pay 75 percent of the state or local government unit's costs for the program.

Fourth, it provided for a variety of ways in which the U.S. Office of Child Support Enforcement in HEW would help the states and localities establish paternity, track the father and then proceed against him.

These include technical advice; clear legal authority for states to proceed against federal employes; the use of Social Security, federal employe and Internal Revenue Service records to locate an absent father and find out where he works, and the use of federal tax records to determine a father's ability to pay child support.

Where state law provides for the use of blood tests and lie detector tests to help determine paternity, the federal government will pay 75 percent of the cost, Hays said.

Where the family wasn't on welfare to begin with, it gets the entire payment, less some small service charge levied by the state. About half the $1 billion a year now being collected goes to welfare families.

There is one substantial dispute over the program - the provision in federal law that a welfare mother must cooperate in establishing paternity and locating the father, unless it is determined that it isn't in the best interests of the child. This is usually the case where there is a genuine fear that an angry or unstable father may wreak violence on the mother or child or both for helping nail him to a support payment.

Long has complained that Califano's department regulations allow too much leeway for a woman to refuse to cooperate without loss of benefits.

However, the American Civil Liberties Union believes there is "potential for privacy invasion in coercing a woman who is receiving welfare to reveal who the father of the child is." This fear is shared by some welfare groups. Some groups representing divorced fathers are also said to be unhappy with the program.

An ACLU spokeswoman said there are reports that some jurisdictions have questionnaires which, if the woman says she doesn't know who the father is, demand to know the names of the men with whom she had sexual relations.

Ed Pitt, a spokesman for the national Urban League, said that group is now assessing its local affiliates to determine whether there is a problem of abuse.

Califano, however, is enthusiastic about the program. He believes the regulations will prevent abuses of privacy. He has told aides to shoot for a doubling of the amount collected under the program - from $1 billion in fiscal 1978 to $2 billion in fiscal 1979.