New Zealand have named three uncapped players in their squad for the one-off Test against Bangladesh in Hamilton next week.

Batsmen Neil Broom and Peter Ingram join late-blooming quick Andy McKay in the 13-man squad.

McKay is arguably the most interesting selection after his stand-out year since moving to Wellington this season.

Black Caps skipper Daniel Vettori has described the 29-year-old as the quickest bowler he has faced in domestic New Zealand cricket, with the left-armer clocking over 150mph.

McKay has impressed after making his one-day international debut in the current series against the Tigers and coach and selector Mark Greatbatch believes he can help fill the void left by retired duo Shane Bond and Iain O'Brien.

"Andy McKay has been a big improver this year with Wellington," he said.

"He took his opportunities in the ODI games he played against Bangladesh and in all formats of the game for Wellington, so now he has a chance to prove himself in the Test arena.

"Andy has some good pace and can move the ball around, which is always going to bother even the best of players."

Greatbatch indicated 31-year-old Ingram, who also made his ODI debut in the current series, will take his place at the top of the order to allow Martin Guptill to move down the order.

Broom is a like-for-like replacement for out-of-sorts middle-order batsman Daniel Flynn.

"Peter Ingram has been picked based on the form he has shown in the longer versions of the game over the last three years of domestic cricket," he said.

"We always had an eye on him for the Test matches and this is his chance to step up.

"The top order is an important area where we need to improve and we want to see how Peter goes at the next level."

He added: "Neil Broom has been picked on the weight of domestic runs he has scored.

"We have moved Martin Guptill down the order. We feel that this is a more natural position for him and he is better suited there.

"He is a quality young player and he needs a chance to play longer innings."

Grant Elliot and Jesse Ryder were not considered because of injury.

Squad: Daniel Vettori (captain), Neil Broom, Martin Guptill, Peter Ingram, Brendon McCullum, Tim McIntosh, Andy McKay, Chris Martin, Jeetan Patel, Tim Southee, Ross Taylor, Daryl Tuffey, BJ Watling.