Lord Ken Maginnis and David Simpson, DUP, had been due to fly out this week to meet soldiers from the Royal Irish and the Irish Guards but the Army couldn't find flak jackets large enough to fit them.
"To be told at the last minute that the British Army has not got two flak jackets with a 54" chest was just a bit thick," said Lord Maginnis who weighs in at about 18 stone.
"I wanted to go out and meet the troops and made considerable efforts to clear my diary.
"So this made me very cross. I am no giant, neither is Davy Simpson. We are both reasonably normal, although we are bigger than most."
Lord Maginnis said the cancelled trip made him "absolutely furious".
"The reality is that we have young men and women out there fighting for us. They are putting their lives on the line. They deserve a little bit of consideration," he said.
Lord Maginnis said he had made the trip two years ago - and he has got lighter since then.
However, in a statement, the Ministry of Defence said: "Nobody is allowed to board an aircraft to Afghanistan without correctly fitting body armour.
"The MoD provides a wide range of sizes but regrettably none was suitable on this occasion.
"We recognise the importance of politicians visiting Afghanistan but this trip has been postponed while we try to source sufficiently sized body armour."
Two of Northern Ireland's politicians are spitting nails after a trip to visit troops in Afghanistan was called off because they were too portly for Army flak jackets.