For Alesi, it will be his debut in an F1 car just over 30 years after father Jean first drove the F1-90 at Fiorano.
Armstrong, who will drive in F2 with DAMS this year, also makes his bow in F1, becoming only the second New Zealander to drive a Ferrari F1 car after Chris Amon who raced for the Scuderia from 1967 to 1969.
Shwartzman, meanwhile, last drove for Ferrari in the young driver test at Abu Dhabi 42 days ago.
Completing the test will be Mick Schumacher, who this year will drive in F1 with Haas, and Callum Ilott, who is now Ferrari's official test driver.
F2 champion Schumacher will drive on Thursday afternoon and Friday morning, providing him with what Ferrari describe as "a chance to do further prep work for his first season in the sport’s top category".
F2 runner-up Ilott completes the running on Friday afternoon.
Ferrari claim that "apart from being helpful for all the drivers, the test is also an opportunity for the team itself to prepare for the one and only pre-season test in Bahrain from 12 to 14 March".
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