With almost two thirds of the Senate paying final tribute, Henry M. Jackson was buried today in the home town where he delivered the local newspaper as a boy and began his political career as a prosecuting attorney.

Vice President Bush, Chief Justice Warren E. Burger, former secretary of state Henry A. Kissinger and about 60 of Jackson's Senate colleagues were among the thousand dignitaries who attended the service at the First Presbyterian Church.

Former senator Warren G. Magnuson, who lost his Senate seat in the 1980 election, welcomed the senators to the state on "this sad occasion."

Magnuson stood across the church from Jackson's flag-draped casket and said: "We served together in the House and the Senate almost half-a-century. We worked as a team shoulder to shoulder. Now that team is dissolved."

Magnuson, Sens. Edward M. Kennedy (D-Mass.) and Daniel Patrick Moynihan (D-N.Y.) and Rep. Thomas S. Foley eulogized Jackson as a man of compassion and a man of the people.

Jackson's children, Anna Marie, 20, and Peter, 17, also gave brief eulogies.

Anna Marie, a student at Stanford University, described how her father helped her with her political science classes.

"I remember one day when he called me from New York," she said. "He insisted on staying on the phone until I understood the history of the New Deal backwards and forwards. That phone call took 2 1/2 hours."

Peter, a high school senior, recalled how his father was "so enormously proud" that as a five-year-old he had memorized the names of all the presidents. He said Jackson frequently stopped voters and other friends and had them listen while the lad recited the names.

Foley, who worked as an aide to Jackson before his election to Congress in 1964, said Jackson was more than a boss.

"He was to his staff a teacher. He taught by example," Foley's voice wavered as he spoke and at one point he paused, saying: "I guess you're never too old to shed a tear for an old friend."

Jackson, 71, died last Thursday of a heart attack at his home here. He was serving his sixth term in the Senate at the time of his death.

Gov. John Spellman, a Republican who must appoint Jackson's successor, refused to discuss the subject until after the funeral. Republican sources say he is expected to name former governor Dan Evans on Thursday.

An opinion issued by state Attorney General Ken Eikenberry said that an election must be held Nov. 8 for the seat; the term runs until 1988. Eikenberry also said no primary election is necessary, setting off a scramble and presumably giving the new incumbent a significant edge if several Democrats challenge him and split the Democratic vote.