* Computer-based training and test involved - union
* First Southwest 737 MAX simulator ready for use in October
* 'Very disturbing' that MCAS system not disclosed earlier - union (Adds details from union statement; paragraphs 4-8)
CHICAGO, March 20 (Reuters) - Extra computer-based training will be required after a planned update to the software on the Boeing Co 737 MAX aircraft, Southwest Airlines Co's pilot union said on Wednesday, adding that it was seeking additional information for pilots.
Boeing has been working on a software update to an anti-stall system called MCAS since a Lion Air plane crashed in Indonesia in October, killing all 189 aboard.
That effort has become urgent after a second 737 MAX 8 crashed in Ethiopia last week, with the death of 157 people, and regulators grounded the global fleet of the aircraft.
Southwest Airlines Pilots' Association (SWAPA) said it had previewed the proposed Boeing training, including a required test at the end, which would be mandatory for Southwest pilots before flying the 737 MAX again.
"It is still very disturbing to us that Boeing did not disclose MCAS to the operators and pilots," the association told members in a memo seen by Reuters.
"This methodology should, and can, be examined....Questions about increased digitization of an existing aircraft should be examined."
The union said Southwest expects to receive its first 737 MAX simulator in July, which should be ready for use around October. The airline should also receive two more 737 MAX simulators in October and three more in January 2021, it said.
A Boeing spokeswoman said training on the software update would be provided by the manufacturer, but declined to disclose further details.
Last week, Boeing said the software update was expected to be deployed across the 737 MAX fleet "in the coming weeks."
(Reporting by Tracy Rucinski; Additional reporting and writing by Jamie Freed; Editing by Clarence Fernandez)