The Commission of Fine Arts yesterday unanimously approved the addition of a flagpole and a sculpture of three infantrymen to the Vietnam Veterans Memorial in Constitution Gardens, but demanded that the proposed locations for the added elements be changed.

Approval of the additions by the commission was the last major legal hurdle for proponents of changes in the controversial memorial.

The sculpture should not be allowed to "shiver naked out there in the field," said commission chairman J. Carter Brown, referring to its proposed location in an open area approximately 170 feet from the apex of the angle formed by the long walls of black granite in Maya Ying Lin's original, competition-winning design.

Instead, Brown proposed that the flagpole, sculpture and third proposed element -- an alphabetical "locator" for the names of the American war dead that are engraved in chronological order of their deaths upon the walls of the nearly completed V-shaped memorial -- be grouped together in a different location to "help enhance the entrance experience of the memorial."

"We're feeling very positive," commented Jan Scruggs, president of the Vietnam Veterans Memorial Fund, immediately after the vote, which came at the end of a long, intense afternoon session conducted before an overflow crowd of more than 200 in the Cash Room of the Treasury Department. "We got the essential approvals that we wanted--the flag and the statue," he said, "and now we can begin the process of getting Vietnam veterans moving behind the memorial again."

Donald Paul Hodel, undersecretary of the Interior, testified before the seven-member commission that the department would grant a permit to dedicate the memorial only if "the compromise design is approved." After the meeting, in spite of the conditions attached to the commission's approval, Hodel said that "it looks good for the dedication -- we're very pleased and would like to commend the commission for its work."

Maya Lin's reaction to the change in location was, she said, "relief, in a small sense." The young designer, who won the competition for the memorial while an undergraduate student at Yale University, said she was most concerned that the new elements "not interrupt the memorial." "I don't know where they will end up," she continued, "but care will have to be taken so you don't have three isolated elements floating in space."

Frederick Hart, sculptor of the statue, called the commission's decision "Solomon-like" in an interview with the Associated Press.

In his remarks prior to the vote, Brown suggested that a "natural entrance" to the memorial, and therefore presumably a location the commission would favor for the cluster of additions, is near the western end of the memorial wall -- a location nearer to the Lincoln Memorial than the proposed site -- and not in direct line with the wall itself.

Brown said the commission could consider a revised proposal from the Vietnam Veterans Memorial Fund for grouping the three elements at its next regular meeting on Nov. 10, which is the opening date of a five-day National Salute to Vietnam Veterans to take place in Washington. Commission member Walter Netsch said the commission would be willing to call a special session to consider an alternative proposal on the location of the new elements. The proposed additions will be considered by the National Capital Planning Commission on Oct. 21.

Lin's original design, selected by a jury from more than 1,400 entries to the competition, foresaw the walls rising gradually from the ground in the glade near the Lincoln Memorial to a height of 10 feet at the apex. The additions were a compromise worked out in sessions sponsored early this year by Sen. John W. Warner (R-Va.), after considerable discontent with Lin's design surfaced among veterans' groups. This compromise plan placed the flag behind the walls about 40 feet from the apex and put the sculpture in the glade in front of the walls, about 170 feet away from the angle.

A parade of witnesses expressed passionate approval of the design changes, or equally passionate opposition, at the commission meeting yesterday before the decision was reached. The meeting was interrupted at dusk as the commission members were whisked by van to visit the memorial site, where eight-foot-high Styrofoam mockups of Hart's statue had been placed in the glade. The dramatic vote was taken when the commission returned from this trip through the rainy streets.

Rep. Don Bailey (D-Pa.), a combat officer in Vietnam, appeared before the commission to plead for the inclusion of Hart's statue and the flag. "You had to have a reason why you were going to tell a kid to do something that might take his life," he said, "and that is what that flag and that statue represent to us." Many other witnesses, some representing national veterans groups, echoed these sentiments.

Most of the witnesses who opposed the changes in the design did so on esthetic grounds. "Esthetics alone matters here today," said Michael Straight, a World War II bomber pilot and former deputy chairman of the National Endowment for the Arts, who testified that the two concepts--Lin's abstract walls and Hart's realistic sculpture -- "cannot be melded."

Robert M. Lawrence, president of the American Institute of Architects, protested that the proposed change "is not a modification of or an addition to the original competition-winning design. It is a new design altogether . . . We should not allow a patched-up, modified, compromised memorial to be built."

When the day was done it turned out that the commission agreed, up to a point. "We wanted to clear those elements out of interfering with the experience" of the memorial as Lin had designed it, Brown said. "We wanted something that pleased all Americans, not just a group of veterans, although we recognized the need for healing and recognition and all of that. But it was up to us to take the long view."