The Israeli Army evacuated its positions in the mountains of eastern Lebanon today, completing the second stage in Israel's planned three-stage withdrawal from Lebanon.

The pullback, from an area of about 470 square miles, meant that for the first time in almost three years Israeli and Syrian soldiers no longer directly confronted each other in eastern Lebanon. Military officials said the new Israeli deployment was about 13 miles from the nearest Syrian units, which until today had been within a few hundred yards of the Israeli line.

The new Israeli line in eastern Lebanon is located several miles north of the Druze village of Hasbaya. The positions the Israelis evacuated today included an observation post and artillery encampments on Mount Baruk, from which Israeli gunners were within range of Damascus.

For more than a year, Israeli officials argued that the radar and gun positions on Mount Baruk would force Syria to acquiesce in a political agreement between Israel and Lebanon. But the Syrians did not budge, forcing cancellation of the agreement signed May 17, 1983, and today the Israelis abandoned their Mount Baruk stronghold.

There were no immediate reports of Syrian troops moving into the area evacuated by the Israelis, and Defense Minister Yitzhak Rabin said he did not expect a major Syrian move toward the south.

"I believe Syria will refrain from doing things that will bring about a direct military confrontation between it and Israel," Rabin said. "They might, here and there, move a little bit towards the south, but they know what could be intolerable to us."

He added that the Syrians, who the Israelis estimate have about 50,000 troops in Lebanon or near the Syrian-Lebanese border, "understand that we have certain limitations beyond which we won't be able to just stand aside."

Reuter later reported from Lebanon that Lebanese Army troops had been deployed in most areas vacated by the Israelis but that Druze militiamen took control of the Mount Baruk peak and Christian militiamen remained in the Jezzin area.

The pullback, which came as Israel observed its Memorial Day in honor of soldiers killed in battle, began at dawn with Israeli units burning the last facilities and materiel left at their outposts. Columns of tanks, armored personnel carriers, trucks and other vehicles lumbered slowly south along the narrow mountain roads while Israeli helicopter gunships provided air cover.

Soldiers who spoke with reporters in the area expressed relief they were leaving, but it was laced with bitterness about their experience in Lebanon.

A soldier who identified himself as Pvt. Amnon, 38, a reservist from Nazareth and a member of one of the first Israeli units to enter Lebanon in the June 1982 invasion, said, "They should shoot former defense minister Ariel Sharon. I was here when the first troops came in. I thought then it was a big mistake. We couldn't win. It was a war we couldn't win."

An Army commander in the area who identified himself as Col. Zvika said, "Israel is strong when its people believe in what it is doing, not because it holds Mount Baruk. In Mount Baruk and this war, the people stopped believing."

At 11 a.m., many of the military convoys halted and the soldiers stood in silence for two minutes to mark memorial day for the soldiers killed in the five wars and several smaller conflicts that Israel has fought since its creation as an independent state in 1948. In Israel, air raid sirens sounded as traffic and other activities came to a halt for the observance.

But at sundown tonight, the mood in Israel changed abruptly as the country began celebrating its 37th independence day.

The Israeli Cabinet voted Sunday to authorize the last stage of the withdrawal plan and said the pullout from Lebanon would be completed by early June.

According to Army figures, the area that was evacuated today has a population of about 60,000, almost half of whom are Lebanese Christians. The evacuated area includes the largest Christian town in southern Lebanon, Jezzin, with a population of more than 15,000. In Jezzin, the withdrawing Israeli columns rolled passed a huge portrait of Bashir Gemayel, the Christian president-elect of Lebanon who was assassinated in September 1982, while the townspeople watched, mostly in silence.

Lebanese Christian militia leaders have suggested that the Israelis maintain a corridor from their security zone in far southern Lebanon to Jezzin to protect the town's Christian residents from nearby Lebanese Moslem and Druze militias and Palestinian guerrillas. However, Rabin made clear today that the Israelis have no intention of intervening directly again in what they consider to be purely local Lebanese conflicts.

"If the Christians manage to keep a corridor open, that is fine with us," the defense minister said. "But we will not activate the Army to do that."