New York (CNN Business) As countries and airlines around the globe ground their 737 MAX planes, Boeing continues to claim its planes are safe to fly.

After the second crash of a 737 MAX 8 plane in less than five months, the aviation authorities in the United Kingdom, Germany, France, Australia, Indonesia, China and other countries have now ordered that none of the planes fly in their airspace.

A growing number of airlines around the globe have announced they won't fly the planes until they know what happened in Sunday's fatal crash of an Ethiopian Airlines jet , which killed all aboard. The cause of Sunday's crash is still under investigation . It follows an October crash in which pilots on a Lion Air flight fought an automatic safety system for control of the plane.

Some airline experts disagree with Boeing's decision.

"Not grounding the jets puts Boeing in a very bad light," said Mary Schiavo, a CNN aviation analyst and former inspector general for the US Transportation Department.

If Boeing ordered a global grounding of the more than three hundred 737 MAX planes in service, and if it halted deliveries of the new jets, it would give the company more control of a situation that is quickly spiraling out of its control, Schiavo said.

"Airlines and countries all over the world are saying this is ridiculous," she added.

Other experts say it will be difficult for Boeing to ground the planes — and grounding the flights might not be the right decision, no matter the public pressure.

"If Boeing and and the FAA feel a plane is airworthy, then why order a grounding?" said Carter Copeland, analyst with Melius Research.

But the longer Boeing waits to act, the more pressure will build from aviation authorities around the world, and perhaps even at the FAA.

"The best time to have [ordered a grounding] was immediately following the Ethiopian Airlines crash," said Nick Wyatt, analyst with GlobalData. "I think now they're concerned they could be seen as wavering from the stance that the aircraft is safe. I don't think they can win either way here."

The cost of grounding all 737 MAX planes could be between $1 billion and $5 billion, according to estimates from Wall Street firms Melius Research and Jefferies.

Both those estimates were based on a three-month grounding. Boeing could afford that cost: It posted record revenue of $101 billion last year, and a $10.6 billion profit. It had forecast even stronger results this year.

Boeing has grounded an entire fleet of planes before. In 2013, Boeing told airlines not to fly their 787 Dreamliners because the planes' batteries were catching fire. At the time, only 50 Dreamliners were in service, so the cost to Boeing was "minimal," the company said.

Boeing didn't even stop building the 787 planes while it worked to find a solution to the problem. The costs of grounding all of its 737 MAX jets and halting delivery until April might also end up being minimal to a company the size of Boeing, particularly if it doesn't lose any long-term sales.

The company isn't budging.

"Safety is Boeing's number one priority and we have full confidence in the safety of the MAX," Boeing said in a statement Tuesday. "We understand that regulatory agencies and customers have made decisions that they believe are most appropriate for their home markets. It is also important to note that the Federal Aviation Administration is not mandating any further action at this time, and based on the information currently available, we do not have any basis to issue new guidance to operators."

Boeing's stock has fallen 11% this week.

The FAA and Boeing both say a software upgrade will give pilots greater control over plane in case problems emerge with the planes' safety systems. That fix is due in April.

The two US airlines flying the 737 MAX 8 — American Airlines and Southwest — say they will continue to fly those planes.

American AAL repeated its earlier statement that it would monitor the investigation of Sunday's crash but it has "full confidence in the aircraft and our crew members."

Southwest LUV said, "We remain confident in the safety and airworthiness of the MAX 8. We don't have any changes planned to our MAX 8 operating plans."

The 737 MAX family of planes is new enough that it doesn't make up a significant portion of airlines' fleets. Southwest had 34 of the 737 MAX 8, out of 750 jets it operates. American Airlines has 24 of the planes, flying 85 flights daily.