* Sunday's disaster kills 157 people from 33 nations
* Second crash involving the Boeing 737 Max 8
* Beijing and Jakarta ground flights, India holds review
* U.N. staff weep, Ethiopia holds day of mourning
* Boeing shares tank nearly 10 percent (Adds India, details from scene, tracking information)
ADDIS ABABA/BEIJING, March 11 (Reuters) - China and Indonesia grounded their fleets of Boeing's 737 MAX 8 aircraft on Monday, and investigators recovered the black box from a crash that killed 157 people, the second disaster in less than five months involving the new model.
At the crash site, men in Red Cross jackets and face masks picked through a large crater, putting items in black paper bags. Clothing, boarding passes, serviettes and other personal effects were scattered over the field along with charred bodies and debris from the shattered jet.
The Ethiopian Airlines jet plunged into an arid field minutes after take-off from Addis Ababa for Nairobi on Sunday, killing all on board. The victims came from more than 30 nations and included 22 United Nations' staff.
The crash follows one of the same aircraft model operated by Indonesia's Lion Air, which went down in October shortly after take off, killing all 189 people on board.
Boeing's share price plunged at the prospect that two such crashes in such a short time could reveal flaws in its new plane. The company has already accepted orders for more than 5,000 of the new, high fuel economy planes, which entered service less than two years ago and are set to be the workhorses for airlines around the globe for decades.
The discovery of the black box with both the cockpit voice recorder and digital flight data, reported by Ethiopian state TV, should shed light on the cause of the crash.
Ethiopia's parliament declared Monday a day of mourning. The dead included aid workers, doctors, professors of literature and botany, a law student, a newly-wed woman, a father soon expecting a child, and a couple who recently had a baby.
In Nairobi, a major hub for aid workers and diplomats in Africa, a summit opened with a moment of silence and tears for the U.N. members killed.
"It is one of the biggest catastrophes we have had in years," said Michael Moller, U.N. head in Geneva.
The 737 line, which has flown for more than 50 years, is the world's best selling modern passenger aircraft and viewed as one of the industry's most reliable.
The new MAX 8 variant, with bigger engines designed to use less fuel, entered service in 2017. By the end of January this year, Boeing had delivered 350 of the new jets to customers, with another 4,661 on order.
Boeing's shares slid almost 10 percent in early trading on Monday. The move, if maintained through normal trading hours, would be the biggest fall in Boeing's stock in nearly two decades, halting a surge that has seen it triple in value in just over three years to a record high of $446 last week.
CHINA'S 'ZERO TOLERANCE'
Two crashes in such a short period involving the same model prompted countries to take swift action.
Ethiopian Airlines, which has four other 737 MAX 8 jets, said it was grounding them as a precaution, although it did not yet know the cause of the crash.
China on Monday ordered its airlines to suspend operations of their 737 MAX 8 jets by 6 p.m. The Civil Aviation Administration of China (CAAC) said it would notify airlines when they could resume flying the jets, after contacting Boeing and the U.S. Federal Aviation Administration (FAA).
The CAAC noted that the accidents involving newly delivered planes both had taken place shortly after take-off.
Indonesia said it would temporarily ground Boeing 737 MAX 8 aircraft for inspection.
Cayman Airways grounded both of its new 737 MAX 8 jets temporarily too, while India announced a safety review and new instructions later on Monday or Tuesday for local carriers.
A senior U.S. official said it was too early to tell if there was any direct connection between the two accidents but assessing that was a priority for investigators.
Ethiopian Airlines said its pilot Yared Getachew, who was a dual Ethiopian-Kenyan national, had a "commendable record" and more than 8,000 hours of flying experience.
The airplane was received in November 2018, had flown more than 1,200 hours, and returned from Johannesburg earlier on Sunday, Chief Executive Tewolde GebreMariam. Nevertheless, Getachew had mentioned difficulties and wanted to return.
It crashed near the town of Bishoftu, 62 km (38 miles) southeast of the capital Addis Ababa, with 149 passengers and eight crew aboard.
The flight had unstable vertical speed after take off, the flight tracking website Flightradar24 tweeted.
Data released by the Sweden-based service suggested the aircraft had climbed almost 1,000 feet after taking off from Addis Ababa, a hot and high-altitude airport whose thinner air requires extra effort from an aircraft's engines.
It dipped about 450 feet before rapidly climbing another 900 feet until the point where satellite tracking data was lost.
(Additional reporting by Maggie Fick, Katherine Houreld and Hereward Holland in Nairobi, Jamie Freed in Singapore, Bernadette Christina Munthe in Jakarta, Josh Horwitz in Shanghai, Sanjana Shivdas in Bengaluru, Stephanie Nebehay in Geneva Writing by Andrew Cawthorne Editing by Peter Graff)