US tax law is a Byzantine tapestry of deductions, credits, rates, and exclusions. This week Congress will begin an examination of the system - a tentative step toward what some hope will be real tax reform.
''We may be witnessing the beginning of a process that, over the next few years, will lead to a simpler, fairer, and economically more productive tax system,'' Senate Finance Committee chairman Robert Dole wrote recently.
On Sept. 28 Senator Dole's committee will begin a three-day series of hearings on the flat-rate tax - a catch phrase that covers various tax-reform proposals. Though Senator Dole has expressed reservations about a pure flat tax and has said such a proposal is unlikely to be seriously considered before 1985, he sees his hearings as opening public debate on the issue.
Senator Dole ''wants to let anybody who has any ideas on these matters get them on the record,'' said an aide. ''There definitely will be further hearings. He would still consider introducing his own legislation.''
In its purest form a flat-rate tax would eliminate all deductions, except perhaps a personal exemption so the poor would not have to pay tax. All income would then be taxed at the same rate - say, 15 percent. Unlike the current progressive tax system, the rates would not rise for higher-income taxpayers.
President Reagan calls the idea ''tempting,'' and economists and politicians say the flat-rate tax currently has strong public support.
The term ''is as popular as motherhood,'' writes Rudolph Penner, American Enterprise Institute economist, in a recent newsletter.
At least 10 flat-tax bills are before Congress, though some are flat in name only. One, introduced by Sen. Bill Bradley (D) of New Jersey and Rep. Richard A. Gephardt (D) of Missouri, carries the somewhat disconcerting label ''progressive flat tax,'' and would reduce the current system's 12 individual income-tax brackets to four while lowering rates across the board and eliminating many deductions.
Economists say public support for the flat tax seems to be rooted in the belief that loopholes allow the rich to escape most taxation. In addition, the average taxpayer believes his tax burden would become lighter under a flat system, says Tom Field, executive director of Tax Notes.
However, says Mr. Field, it's unlikely a flat tax will become law.
''There's a deep-felt public revulsion about the state of the tax system,'' he said. ''But the closer a flat-rate tax gets to enactment, the further from enactment it will actually be, because more people will look at it and decide they don't like it.''
In the first place, say economists, any reasonably flat tax would shift much of the nation's tax burden to the shoulders of lower-income taxpayers.
''It would be a bonanza for the rich,'' says Joe Pechman, Brookings Institution director of economic policy.
A flat tax of 16 percent, with the personal exemption the only deduction, would raise the same amount of revenue as the current system, estimates Henry Aaron, another Brookings economist. Under such a system, average taxes for those who make less than $50,000 would increase, says Mr. Aaron. Those who make more than $50,000 would pay less in taxes.
In the second place, eliminating all tax deductions (''preferences,'' in congressional parlance) would require a political struggle so furious it would make this year's tax fight look like a Sunday volleyball game.
''There are huge constituencies out there that would be enraged,'' said Mr. Field.
Tax preferences currently cost the federal government $250 billion a year. But these ''loopholes'' include home-ownership deductions, deductions for charitable contributions, and other items untouchable for political considerations. Any flat tax that retained homeowner and charity deductions would need at least a 20 percent across-the-board rate, estimates Mr. Field - even if it eliminated preferential tax treatment for medical and casualty expenses and social-security payments.
Sen. Russell B. Long of Louisiana, ranking Democrat on the Finance Committee, often points out that simplification of the tax code and flat rates are two completely separate issues.
For instance, Brookings economist Pechman estimates that tax rates could be reduced an average of 22 percent by 1984, if ''unnecessary'' exclusions, deductions, and exemptions are stricken from the tax code.
Depending on the definition of income and what deductions are retained, says Pechman, a progressive tax system with rates ranging from 9-12 percent to 28-30 percent could raise the same amount of revenue as the current system.