President Reagan, in a radio address just two days before the income-tax filing deadline, promised today that his forthcoming tax simplification plan would cut most Americans' income taxes.

Reagan offered no new details of the proposal, which he said he will unveil after he returns from Europe in May.

Last December the Treasury Department proposed to cut individual tax rates while eliminating many individual deductions and many tax breaks for corporations. A revised plan is being worked out by Treasury Secretary James A. Baker III.

"We expect to advance a proposal that can win bipartisan approval this year," Reagan said.

Reagan said he would cut the maximum individual tax rate, which is now 50 percent, to 35 percent "or lower," and would "increase significantly" the personal exemption. He added that "we'll reduce corporate rates, too."

The president has pledged that the plan would be "revenue neutral."

Reagan said today he will accomplish this by "broadening the base -- in other words, eliminate the shelters that make tax avoidance legal."

Reagan reiterated that he would not eliminate the home-mortgage interest deduction.

He added that, "over the years the entire tax system has come to mirror Washington itself: a complicated, frustrating, unfair mystery of legalistic gobbledygook and loopholes never designed, it seems, to help everyday wage earners, only those who can afford high-priced attorneys and accountants."