The Senate Finance Committee's radical tax-overhaul bill contains a hidden provision obligating the U.S. Treasury to write hundreds of millions of dollars of checks to ailing steel companies over the next several years.

The provision, which has not yet been released to the public, is one of several dozen "transition rules" aimed at easing the adjustment of companies and people to a new tax system. It would save for most steel firms a portion of the investment tax credit, a subsidy for equipment purchases that is being repealed.

Many of the proposed transition rules are still being crafted, but congressional and industry sources said they would provide exceptions for downtown rehabilitation projects, trash-to-steam plants, cellular phones, restaurants, oil companies, subway cars, airplanes, office towers, apartment complexes, telecommunications lines, coal-fired and hydroelectric power plants and many others.

Taken together, such exceptions to the committee's bill would be worth $5.5 billion to their beneficiaries by 1991. They were as hard-fought -- and at least as heavily lobbied about -- as major provisions in the legislation that passed the committee last week.

But the action took place behind closed doors, where Finance Committee Chairman Bob Packwood (R-Ore.) decided which groups would be eased into the new system of fewer deductions and lower rates, and which would make the shift abruptly. Many of the proposed rules may be revised, according to congressional sources.

Meanwhile, Packwood moved yesterday with Senate Majority Leader Robert J. Dole (R-Kan.) and Sen. Russell B. Long (D-La.) to protect the committee's tax package from a raft of amendments expected when it is taken up on the Senate floor in June.

"Each of us will receive enormous pressure from many interest groups to make concessions," the three senators wrote their colleagues. ". . . We ask you to keep an open mind and reserve your commitments until you have had an opportunity to review the committee's bill in its entirety," they added.

Also yesterday, the Council of Economic Advisers said the Finance Committee bill would boost the economy by increasing the number of new jobs by 4 million in the next 10 years. Inflation-adjusted economic growth would be 2.5 to 3.2 percentage points higher than it would otherwise be in 10 years, according to what a senior administration official called the CEA's "guesstimate."

The transition rules in the Finance Committee bill are significantly more modest than the $25 billion of exceptions passed by the House last year. Such rules, a routine part of any tax law, are designed to prevent economic shock effects and at times to win supporters.

The steel rule appeared to be the most extravagant, carrying a price tag of about $500 million over five years, according to several sources. While the committee bill would abolish the investment tax credit, which subsidizes up to 10 percent of the cost of new equipment, the rule would effectively let the steel industry "cash in" about $1.4 billion of unused credits, receiving 50 cents on the dollar.

The rationale, according to industry officials, is that the investment credit creates tax write-offs only for those who pay taxes. Because the steel industry has suffered sustained losses, most steel makers have accumulated tax credits but have no tax liability against which to use them. Without a special rule, most of the credits would expire unused, industry officials said.

So while other industries could use the credit only against taxes from three previous years, the proposed rule would allow the steel industry to use it against taxes from the early 1970s, its last healthy period, to the present. The government thus would write checks to such firms as Bethlehem Steel, Inland Steel, Armco, LTV and others, repaying them for some past taxes.

The rule, pushed by Sen. John Heinz (R-Pa.) and John C. Danforth (R-Mo.), resembles an earlier proposal by Packwood to allow all industries to "cash out" unused investment credits at a 30 percent discount. That approach was discarded after a public uproar over the prospect of the Treasury writing checks to profitable corporations. Steel, however, is not profitable, industry officials argued.

"We got something other people didn't because we're in more trouble than they are and we really are a deserving case," said a steel industry executive.

But others would receive plenty. Thanks to Sen. David L. Boren (D-Okla.), for example, Oklahoma-based Phillips Petroleum would get a $100 million reduction in taxes that the bill would have imposed on its recent corporate restructuring and would get protection for an investment tax credit on a $2 billion project in Point Arguello, Calif. Other Boren-backed transition rules would help a coal plant in Poteau, Okla., and a telecommunications project for Tulsa-based Williams Co.

Sen. Charles E. Grassley (R-Iowa) asked for the investment tax credit for purchases of equipment by a restaurant in Cedar Rapids.

Sens. Max Baucus (D-Mont.) and George J. Mitchell (D-Maine) got an extension of the investment credit for companies building hydroelectric and co-generation plants.

Sen. Bill Bradley (D-N.J.) preserved tax benefits for the construction of plants that convert garbage to energy.

Sen. Daniel Patrick Moynihan (D-N.Y.) saved taxes for a Merrill Lynch office headquarters, Pan American World Airways' new jets, New York City's buses and subway cars and a New York State Power Authority project.

"Everybody's got dogs in there," joked an aide to a Finance Committee member.