President Anwar Sadat received an exuberant, shouting welcome from his people tonight as he returned from his peace mission to Israel.

Hundreds of thousands of Egyptians dance, sang and chanted of peace as Sadat rode through the streets of Cairo in an open Cadillac limousine. Some estimates placed the number of people at nearly three million.

Once again Sadat appeared to have read the mood of the country correctly and shored up his domestic support by a spectacular move in foreign policy, a pattern he has followed throughout his seven-year presidency.

Buses rolled into Cairo from all over Egypt this morning, bringing people from the countryside to greet the president. They were joined by residents of the capital who lined the flag-draped 13-mile route from the airport to Sadat's house in the suburb of Giza.

"Sadat, we are with you" and "Sadat, hero of peace," the crowds shouted.

Cairo was in a festive mood anyway, because this is the biggest religious holiday of the year. Nevertheless, Egyptians said there was no doubt that the tumultuous welcome for Sadat represented a genuine outpouring of feeling and a statement of their desire to put an end to the wars that have crippled this country for 30 years.

Only 48 hours before, Sadat had slipped out of the country without fanfare from an obscure military airport near the Suez Canal, leaving behind some apprehension about how his bold venture would be received by the Egyptian people. Aside from a small group of leftist intellectuals and some disgruntled Nasserites, there has been hardly a word of criticism or dissent.

Sadat, a former journalist, is a master at the use of the media to build his image, and no effort was spared to give the Egyptian people every detail of this trip.

Egyptian newspaper have convered the trip exhaustively. Sadat's arrival in Israel, yesterday's speeches in the Knesset, today's joint press conference with Israeli Prime Minister Menahem Begin and the president's return were all carried live on television and radio. All over Cairo, the traditional patterns of family visits and feasting on this day were disrupted as people gathered around their television sets.

On the streets, crowds poured out of the teeming neighborhoods to shout, "Long live Sadat" and to sing patriotic songs as they surged along beside his car. Sadat stood waving and smiling, apparently relaxed and enjoyed the acclaim.

Sadat was greeted at the airport by several top officials of his government, including Prime Minister Mandouh Salem, Speaker of the People's Assembly Sayed Marei and most importantly a relaxed, joking minister of war, Gen. Mohammed Abdel Ghani Gamassy who headed a delegation of about a dozen high-ranking officers.

Two little girls in identical gray and white outfits presented flowers, and Sadat then shook hands with members of the People's Assembly who had come out to greet him. Sadat is expected to address the People's Assembly, Egypt's Parliament, on Saturday to give them the results of his trip.

The virtually complete calm that reigned in Egypt during Sadat's visit to Israel and the Uproarious return appeared to lay to rest any fears that Sadat's gesture would be unpopular or lead to large scale dissent here. On the contrary, it appears to have given him the kind of boost he has needed every since the food price riots of last January challenged the authority of his government.

But none of this could completely mask the anxiety and disappointment among informed and sophisticated Egyptians over the apparent lack of substantive results from the trip.

There were mutual pledges between Sadat and Begin that there would be no more wars between the two countries, and Begin did acknowledge that there are Palestinian Arabs who will have to be heard in the course of peace negotiations.

On the issue that really matters to Egypt, however, the territories occupied in the 1967 war, observers here saw no sign of movement. This gloomy assessment was reinforced by Egyptian journalists who made the trip to Israel. They said they believed Sadat got little if anything in his private talks with Begin that was not made public in their statements to the press.

Both Sadat and Begin said the purpose of this trip was not negotiations toward a peace treaty and warned against expecting too much, but many Egyptians were hoping that Sadat would at least come home with something to show the other Arab leaders to justify the trip they have criticized so strongly.

There was considerable uncertainty here about what happens next.

While the United States, Israel and Egypt all say they favor the reconvening of the Geneva Middle East peace conference, many analysts here believe that the rupture between Egypt and Syria over the trip and the refusal of Israel to deal with any representative of the Palestine Liberation Organization would make it difficult to go to Geneva now.

Foreign ambassadors were not invited to the airport to see Sadat come home tonight, apparently because it was clear to the Egyptians that some would have refused to come and others would have found themselves facing an embarrassing decision.

Among the latter are Jordan and Saudi Arabia, which have good relations with Sadat and have refrained from direct criticism of the Israel trip, but would probably not want to be thought of as having endorsed it.

Sadat dismissed the strong criticism of him that has been heard from some Arab countries by pointing out that it was much worse after he signed the Second Sinai disengagement agreement with Israel in 1975. It took long, bitter negotiations, the war in Lebanon, and the careful diplomacy of Saudi Arabia to heal that split. Whether the current one will blow over, as the Egyptians believe, is not yet clear.

The Cairo press has reported that Sadat is planning to send his vice president, Hosni Mobarak, on a tour of Arab capitals to explain Egypt's position and brief them on the results of the trip.

It was announced tonight that Sudanese President Jaafar Nimeri, probably the Arab leader who is closets to Sadat personally, is to arrive in Cairo Tuesday for consulations.