Boeing ousted one of its top executives on Tuesday, the most significant management change the airplane maker has made as it struggles to contain the crisis following the crashes of two 737 Max jets that killed 346 people.

The executive, Kevin McAllister, was the head of Boeing’s commercial airplanes division. He had been at the center of the company’s response to the crashes and its troubled efforts to return the Max to service after regulators grounded it. This month, The New York Times reported that he was under scrutiny inside the company for his poor handling of relationships with airlines, and his management of the commercial division, which is Boeing’s largest business.

The ouster was Boeing’s most direct effort to hold someone in senior leadership accountable for the bungled handling of the Max crisis, which continues to spiral out of control. The company’s board stopped short of removing Boeing’s chief executive, Dennis A. Muilenburg, though it stripped him of his title of chairman just over a week ago.

The decision to remove Mr. McAllister was made while the Boeing board met in San Antonio on Monday. With directors and senior executives gathered for tense meetings at the plant where the company builds Air Force One, Boeing’s stock took a beating. Two analysts issued downgrades and shares plummeted to their lowest level in more than three months.