Warwickshire opener Dominic Sibley is rewarded for his remarkable summer with a place on the plane alongside Kent batsman Zak Crawley and Lancashire duo Saqib Mahmood and Matt Parkinson.
Batsman Jason Roy is another to miss out after a difficult Ashes series while seamer James Anderson remains unavailable due to a calf injury.
Surrey batsman Ollie Pope is back involved and Jos Buttler will be the wicketkeeper in New Zealand due to Bairstow’s absence.
Mahmood and Parkinson are also in the Twenty20 squad for the five-match series, along with Somerset wicketkeeper-batsman Tom Banton and Worcestershire seamer Pat Brown.
Banton has burst onto the scene this season, hitting 549 runs in the Vitality Blast, while Brown took 17 wickets as Worcestershire reached the final at Edgbaston last weekend.
Mahmood and Parkinson helped Lancashire finish top of the North Group before their quarter-final exit, taking eight and 21 wickets respectively.
Eoin Morgan, who led England to 50-over World Cup glory earlier this summer, will also continue to captain the T20 side.
Mayank Agarwal scored his second double century as India dominated the second day of their Test against Bangladesh in Indore.
Stokes, Buttler and Archer will be captained by Steve Smith for Rajasthan.
Ben Stokes has no desire to be England captain, saying: “It’s just not one of those things I’m desperate to do.”
An England cricket fan talking about the Nineties, won’t be talking about a decade, but a phenomenon.
What were you doing when you were sixteen? You weren’t making your Test debut at the Gabba.
New Zealand bowler Lockie Ferguson is confident he can cause “a little bit of anxiety” in England’s batsman.
Joe Root is realistic about his World T20 chances…
England captain Joe Root has preached the virtue of patience in a new approach under Silverwood.
Good for the series, bad for England…
England’s bowlers were given a stiff workout on another flat pitch in Whangarei…