New York (CNN Business) In the wake of the 737 Max crisis , two leading shareholder advisory firms are urging Boeing stock owners to shake up the company's management and board.

ISS and Glass Lewis, leading research firms that advise investors on how to vote on proxy questions, are supporting a resolution that would split the CEO and chairman positions. Both jobs are currently held by Dennis Muilenburg . The vote will take place at the April 29 annual meeting in Chicago.

The ISS note to investors specifically mentions the two fatal crashes of the 737 Max and the damage to Boeing's reputation from the plane's problems.

"Shareholders would benefit from the most robust form of independent oversight to ensure that the company's management is able to regain the confidence of regulators, customers and other key stakeholders," said the ISS note.

Glass Lewis recommended a vote in favor of the resolution, citing its belief that shareholders are almost always better off if the two positions are separate. It didn't mention the 737 Max issue in the discussion of that resolution.

Glass Lewis recommends shareholders vote against one of the directors, Lawrence Kellner, because of his position as head of the board's audit committee. It said Kellner and the board should have had better oversight of Boeing management as the 737 Max was developed and the crisis unfolded.

"The incidents have already had a substantial negative impact on the company's sales and reputation," Glass Lewis said in its note. "Considering the loss of lives in the accidents, the reputational harm to the company, and the negative impact on future sales of the aircraft, we believe these incidents indicate a potential lapse in the board's oversight of risk management."

The advisory firm said it believes the audit committee should have taken a more proactive role in identifying the risks associated with the 737 Max.

Boeing BA opposes the resolution to split the chairman and CEO positions, and recommends votes for all the current directors, including Kellner.

Earlier this month, Muilenburg announced the formation of a new board committee made up of independent directors charged with reviewing policies and processes for the design and development of its airplanes. He said the committee would recommend improvements to the company's procedures.

The resolution to split the Boeing CEO and chairman positions was submitted well before the second crash of a 737 Max jet on March 10. There was a similar resolution put to shareholders a year ago. It was defeated with the support of only 25% of the company's shares at that time.