The 1984 Reagan budget that goes to Congress Monday is expected to propose cuts of 13 percent for the National Endowment for the Arts and 14 percent for the National Endowment for the Humanities--a victory for the national arts lobby over an administration that started out two years ago trying to cut the endowment budgets in half.

"Apparently we've been able to reverse the direction [in] which the administration has been going, but it's still inadequate," said Rep. Sidney Yates (D.-Ill.), the powerful chairman of the House subcommittee that oversees arts appropriations. Yates has been a strong advocate of increased funding for the endowments.

Last year the administration proposed 26 to 30 percent cuts for the endowments, and the year before the proposed slashes were even more brutal--51 percent for each agency. But each time, led by Yates, Congress restored most of the money.

Administration officials confirmed last night that the figures represent a sharp change in direction.

"In a number of cases in the budget where, in the past two years, experience has revealed strong congressional resistance to deep cuts, we're simply going to face the reality," said an administration official who asked not to be identified. "There will be other instances in which . . . we will recognize congressional priorities and sensitivities and not again propose deep cuts."

Even so, the administration has achieved a reduction in the once-burgeoning budgets of the two agencies that were set up in 1965 to promote the arts and humanities in America, mainly by distributing federal grants to artists and scholars.

This year's arts endowment budget of $143.9 million is $14.9 million less than two years ago. The humanities endowment's $130.1 million this year represents a $21.2 million drop over the same period.

Arts endowment chairman Francis S.M. Hodsoll and humanities endowment chairman William J. Bennett could not be reached for comment last night. The figures contained in the administration's 1984 budget have not been released officially, but were obtained from reliable sources in the government.

Both Hodsoll and Bennett have walked a policy tightrope since being named by Reagan to take over the agencies. While officially they must be advocates for their agencies, they also have been required to support the administration's proposed cuts in the past and, for that, endure the wrath of some members of Congress.

"Would you favor an increase? Would it help the humanities?" Yates demanded of Bennett in a hearing last April.

"No, I would not favor it," Bennett answered. "In answer to the second question, it depends on how we would spend it." Yates then asked sarcastically, "Would you be able to spend it?" and got an equivocal answer.

In another hearing last March, Yates scolded Hodsoll: "Was it necessary, when you took the job, to agree to accept these cuts and go out and defend them?"

People who know them say that privately, neither man has relished the required role.

Bennett, a scholar himself, is said to be devoted to his task of furthering scholarship in America and public understanding of it. Last December he succeeded in getting himself and the directors of several big libraries, to which the endowment is giving millions of dollars, invited to the White House. "I want to take this occasion to express my personal commitment to the humanities," President Reagan told the group.

Hodsoll was a top White House aide before taking over the arts endowment in November 1981, and many in the agency feared he was coming to do a hatchet job. In fact, Hodsoll has become known in the arts community as a moderate advocate of federal arts funding.

Yates said last night the new 1984 figures still represent "a cut . . . They'll talk about the increase over what they proposed last year . . . If there has been a reversal, I'm pleased there has been this total change in attitude, but it's still inadequate."