The Carter administration is running into serious opposition on its highly-touted proposal to reduce the "double taxation" of corporate dividends.

Several tax experts - even some who support the idea in principle - have complained that the Carter proposal is too complex and difficult to administer.

Moreover, many contend it actually would do little to relieve the present problem - that much of corporate earnings are taxed twice, first as profits and later as dividends.

Some tax experts - and businessmen as well - are urging the administration to scrap the proposal entirely and simply enlarge its plan for a cut in the corporate rate.

Joseph A. Pechman, the Brookings Institution tax expert, brands the Carter proposal "an absolute morass." And members of the Business Roundtable have denounced it.

As it stands now, the administration's recommendation falls far short of what President Carter promised as a candidate in last year's election campaign.

Carter's pledge on the hustings was flatly to eliminate double taxation entirely. The proposal was bally-hooed as a major element in his coming tax-revision plan.

But the administration pared this back drastically after tax-drafters made clear how expensive such a move would be. Some estimates placed the cost at $15 billion.

The Treasury now has proposed giving shareholders a tax credit of up to 20 per cent of the dividend they receive - a meager, but clearly more affordable compromise.

In theory, the corporation would continue to pay taxes on the money it distributes as dividends. But the shareholder would be relieved of having to pay the tax again.

The credit would be passed along by the company sending a yearend form to each shareholder telling him the dollar amount of the credit to which he's entitled.

The shareholder then would attach the form to his income tax return and claim the credit allowed. (The firm would send a duplicate to the Internal Revenue Service.)

The procedure seems simple. However, the Carter proposal first would have the shareholder count the tax credit as income before using it to offset his tax bill.

Then under either of the two methods now being considered, the proposal requires taking account of differences in the effective tax rate each firm pays.

Either method could prove to be a nightmare. In one alternative, the shareholder would be entitled to a credit only if the firm pays enough taxes to justify it.

Under a second, the portion of the company's tax payment that the shareholder adds to his income would vary with each firm. Having shares in several firms could be complex.

Administration official explain it with the following example. A taxpayer in the 25 per cent bracket owns 1,000 shares of stock that pays a 50-cent dividend.

Under present law, the individual would pay $125 in taxes on $500 in dividends. With the new Carter proposal, he would pay $50, a savings of $75.

(The computation: The 50-cent dividend on 1,000 shares yields income of $500. In the 25 per cent bracket, the tax would be $125. The 20 per cent credit would be $100.

(Add the total amount of the credit to the income to get $600. Take 25 per cent of that - the taxpayer's bracket - to get $150. Substract the $100 credit. Total tax: $50.)

However, the credit would be available only if the firm paid a reasonably high effective tax rate, and did not pay too much of its earnings out as dividends.

If the company had paid an inordinately low proportion of its earnings in taxes and had an unusually high dividend payout, it would have to make a choice.

Either it would have to pay more in taxes to satisfy a treasury formula for deciding how much a firm must pay to qualify its shareholders for the full credit, or less it must reduce the credit.

As a result, some shareholders maybe receiving a tax credit that is smaller than the 20 per cent the Treasury is proposing as a maximum.

And a taxpayer with a portfolio that includes stocks from several corporations, all with varying effective tax rates and dividend payouts, could wind up with varying credits.

To be sure, the computation would be eased somewhat for the taxpayer because the credits all would be expressed in dollars, rather than in percentages.

Officials say they are working out a liberal enough formula so only a relatively few corporations would fall to quality for the maximum 20 per cent rate.

Understandably, with that kind of complexity, the administration still has not decided on a firm formula. Tax drafters still are experimenting with several proposals.

But tax experts caution that unless the final plan comes out a good deal simpler, the proposal could end up in trouble in Capitol Hill.