Two key members of the Senate Finance Committee introduced legislation yesterday designed to clamp down on the growing number of people who fail to pay taxes from such sources as capital gains, dividend and interest payments and tips.

Sens. Robert Dole (R-Kan.), chairman of the committee, and Charles E. Grassley (R-Iowa), chairman of the Internal Revenue oversight subcommittee, contended that their bill, if enacted, will significantly slow the growth of taxpayer noncompliance, the estimated cost of which has gone from $21 billion in 1973 to $76 billion last year.

The proposal immediately was praised, but not quite endorsed, by Treasury Secretary Donald T. Regan, who described it as "a serious attempt to close tax-compliance loopholes and to arrest the problem of the so-called tax gap. I applaud their effort."

The administration has proposed required 5 percent withholding of interest and dividend income, a method of raising revenue that Dole and Grassley did not include in their plan. Regan said he continues to support the withholding plan, although it faces almost certain defeat in Congress.

In describing the legislation, Dole disclosed that the most recent estimates of noncompliance suggest that 44 percent of the income from capital gains, or $5.5 billion in lost taxes, goes unreported to the IRS. This is more than double previous estimates of 20 percent.

All told, the measure would raise a total of $3 billion in 1983, $8.1 billion in 1984 and $9.3 billion in 1985. If approved by the Finance Committee, it may be attached to the debt-ceiling bill in April as part of a larger effort to raise money.

The major provisions of the legislation are:

* The securities and commodities industries would be required to report clients' capital gains to the IRS. The reports, which would include the clients' Social Security numbers, would give the IRS a basis for computerized checking of taxpayers' reports.

* Similarly, existing reporting of some interest and dividend payments would be extended to include all interest-bearing instruments, including bearer bonds and federal debt obligations.

* State governments, in turn, would be required to report to the IRS any refunds they made to taxpayers. Persons who itemize their federal reports often do not include state refunds in their taxable income.

* Firms employing more than five persons who receive tips would be required to report the tips when they include amounts charged through credit cards.

In addition, the legislation would toughen penalties in a number of circumstances to make it more costly for taxpayers who either attempt to avoid or delay payment of liabilities to the Treasury. These include:

* Without any requirement of showing negligence or fraud, the IRS could impose a 10 percent penalty on persons who significantly claim excessive benefits from tax shelters. The penalty would be assessed against "well-advised taxpayers who take unsupportable positions on their returns while gambling that their tax return will not be audited," Dole said.

* Interest on late payments (and on refunds) will be calculated on a compound basis, rather than simple interest. In addition, taxpayers who purposely delay collection of refunds on net operating losses to pick up a 20 percent interest rate on the refunds, no longer will be allowed to use this tactic in effect to make money from the tax system.

* Corporate managers who commit fraud in behalf of their company will be subject to civil fraud penalties.

The legislation did not touch on the issue of tax payments from independent contractors. Dole said he plans to introduce legislation on this subject next week.