* Ethiopia says data shows similarities with Indonesia disaster
* Question marks over 737 MAX design and vetting
* Boeing promises software update for grounded planes
By Maggie Fick and Tim Hepher
ADDIS ABABA/PARIS, March 18 (Reuters) - The world's biggest planemaker faced escalating pressure on Monday after Ethiopia pointed to parallels between its crash and one in Indonesia, sharping the focus on the safety of software installed in Boeing 737 MAX planes.
The Ethiopian Airlines disaster eight days ago killed 157 people, grounded Boeing's marquee MAX fleet worldwide, and sparked a high-stakes inquiry for the shaken aviation industry.
Ethiopian Airlines, whose reputation also hinges on the investigation, said at the weekend initial analysis of the black boxes showed "clear similarities" with a Lion Air flight from Jakarta in October which crashed killing 189 people.
Both planes were MAX 8s and crashed minutes after take-off with pilots reporting flight control problems.
Under scrutiny is a new automated system in the MAX model that guides the nose lower to avoid stalling.
Lawmakers and safety experts are asking how thoroughly regulators vetted the system and how well pilots around the world were trained for it when their airlines bought new planes.
Ethiopian Transport Ministry spokesman Muse Yiheyis said on Sunday that data recovered from the black boxes by investigators in Paris demonstrated parallels with the Lion Air crash and had been validated by U.S. experts.
U.S. officials did not corroborate that.
With the prestige of one of the United States' biggest exporters at stake, Boeing has said the MAX series is safe, though it plans to roll out new software upgrades shortly.
Boeing has lost billions of dollars of market value since the crash, and halted deliveries of its best-selling model, one intended to be the industry standard but now under a shadow.
There were more than 300 MAX airplanes in operation at the time of the Ethiopian crash, and nearly 5,000 more on order.
Media reports heaped further pressure on Boeing.
The Seattle Times said the company's safety analysis of a new flight control system known as MCAS (Maneuvering Characteristics Augmentation System) had crucial flaws, including understating the power of the system.
It also said the Federal Aviation Administration (FAA) followed a standard certification process on the MAX rather than detailed extra inquiries. The FAA declined to comment, but has said the process followed normal process.
The Wall Street Journal reported that federal prosecutors and U.S. Department of Transportation were scrutinising the FAA's approval of the MAX series, while a jury had issued a subpoena to at least one person involved in its development.
Boeing and the FAA declined to comment on that.
Last week, sources told Reuters that investigators found a piece of a stabiliser in the Ethiopian wreckage set in an unusual position similar to that of the Lion Air plane.
Ethiopia is leading the probe, though the black boxes were sent to France and U.S. experts are also participating.
It was unclear how many of the roughly 1,800 parameters of flight data and two hours of cockpit recordings, spanning the doomed six-minute flight and earlier trips, had been taken into account in the preliminary Ethiopian analysis.
In Addis Ababa, a source who has listened to the air traffic control recording of the plane's communications, said flight 302 had an unusually high speed after take-off before it reported problems and asked permission to climb quickly.
The inquiry is not only crucial to give some closure to the families of the victims, who came from nearly three dozen countries, but also has huge financial implications for Boeing and its many customers worldwide.
The MAX is Boeing's best-selling model ever, with a backlog of orders worth well over $500 billion at a list price of $121 million each.
Norwegian Airlines has already said it will seek compensation after grounding its MAX aircraft, and various companies are re-considering orders.
Some airlines are revising financial forecasts, too, given the MAX had been factored in as providing some maintenance and fuel savings.
Boeing Chief Executive Dennis Muilenburg sought to allay some fears at the weekend.
"While investigators continue to work to establish definitive conclusions, Boeing is finalising its development of a previously-announced software update and pilot training revision that will address the MCAS flight control law's behaviour in response to erroneous sensor inputs," he said.
Dozens of aviation authorities had grounded the MAX series before acting U.S. FAA boss Daniel Elwell said the United States would do the same.
One source close to the probe said Ethiopian officials had been reluctant to share information with U.S. investigation teams and the planemaker.
"There was a lot of distrust, especially at first, but it is easing," the source said, asking not to be named.
There have also been arguments over access to the crater left by the explosive high-speed impact of Flight 302.
The agony for families of the dead in Ethiopia has been compounded by their inability to bury remains. Charred fragments are all that remain and DNA testing may take months.
Writing by Andrew Cawthorne; editing by Jason Neely