Challenged by revived Soviet diplomatic activity in the Mideast and concerned that it soon may be too late for any new Reagan administration peace initiatives, Secretary of State George P. Shultz flies to the Middle East tonight for the first time in 29 months.

State Department officials are making every effort to limit expectations that Shultz will be able to produce a breakthrough in the long-stalled process of finding negotiated solutions between Israel and its Arab neighbors. Given the complex situation, especially Israeli Prime Minister Yitzhak Shamir's seemingly intractable stand on major issues, officials say it will be a notable success if Shultz is able to achieve even modest movement.

Shultz is officially reported to be taking some U.S. ideas in his kit bag when he departs from Andrews Air Force Base late today for Israel, his first stop on a trip that will eventually take him to Moscow next week. All indications are that these ideas center on "interim arrangements" to provide more local autonomy and Jordanian participation in the Israeli-occupied West Bank and Gaza, currently the site of strikes and demonstrations.

The drive for Mideast peace has made little or no progress since Shultz made his last foray to the Middle East in May 1985, and in some respects it seems to have lost ground. On his last trip, Shultz was carrying a list of Palestinians who might credibly participate in negotiations with Israel as part of a joint delegation with Jordan, but none of the names was acceptable to all sides. Since then, discussion has centered on a less tangible issue: whether an international conference convened by Washington, Moscow and other major powers should be the formal sponsor of the eventual negotiations.

Twenty-nine months away from personal diplomacy in the region is an absence of unprecedented duration by a secretary of state since the United States became deeply involved in Arab-Israeli negotiations following the 1973 war and oil embargo. The current trip that some are calling "Shultz's last gasp" is necessary now because soon it will be considered too late to get anything started in Mideast diplomacy while the Reagan administration remains in power.

Last April, Israeli Foreign Minister Shimon Peres made a fervent appeal for Shultz to travel to the area to work at restarting the peace process through a big-power international conference, and Shultz was seriously considering it. However, Israel's Shamir, who opposes this route to negotiations, sent an emissary who persuaded Shultz not to come. Shamir said again yesterday in Israel that he is confident Shultz "won't try to pressure us" to participate in an international conference.

Meanwhile, some of the most striking Mideast developments have been made in Moscow, a fact which has not been lost on any of the nations of the region and which generated increasing pressure for Shultz to show signs of action.

In April Soviet leader Mikhail Gorbachev chose a meeting with Syrian President Hafez Assad to declare publicly that the absence of diplomatic relations between the Soviet Union and Israel "cannot be considered normal." This summer Moscow sent a consular delegation to Jerusalem for the first time since relations were broken off in 1967.

In September at the United Nations, Soviet Foreign Minister Eduard Shevardnadze surprised Peres, his Israeli counterpart, by offering to establish diplomatic interest sections, just short of formal embassies, in one another's capitals. Peres turned down the bid, holding out for resumption of full diplomatic relations.

Despite this and other overtures, including the continuing release of well-known Soviet Jews for emigration to Israel, the Soviet Union still keeps its distance in other ways. On Tuesday, it voted with most of the Arab world to exclude Israel from the U.N. General Assembly, as it has in earlier years.

As the vote suggests, Moscow has also been busy mending fences in the Arab world, sending high-level emissaries to the area and consolidating its influence with the PLO.

In March, the Soviet Union agreed to reschedule Egypt's $3 billion debt from the days when Moscow was Cairo's key military supplier and international patron. Just yesterday Soviet Deputy Foreign Minister Yuli Vorontsov was capitalizing on warmer relations by meeting in Cairo with Egyptian officials, and jointly pledging to pursue "identical views" about the international peace conference. Shultz will arrive in Cairo Monday to see the same officials.

In recent months, both Washington and Moscow have also been deeply engaged in the Persian Gulf in ways that affect their other Mideast relations. Moscow is trying to balance closer ties with Iran against improved relations with Iran's Arab foes, which may explain the Soviet desire for delay in voting a U.N. arms embargo against Iran.

Saudi Arabia, which Shultz will visit on a brief trip Saturday, was shocked by the revelation that the Reagan administration had been secretly selling arms to Iran. King Fahd is said to have important questions about U.S. intentions and staying power in the gulf, along with less urgent questions about Washington's role in seeking to revive the Mideast peace process.