Some farmers say they will stop soldiers using land in mid and west Wales in protest at the hunting ban.
Up to 200 soldiers will be involved in the exercise in Wales
Exercise Pilgrim's Progress is set to take place in the area in late October and November and the army has asked people for consent to use their land.
The issue was raised at the AGM of the Carmarthen branch of the Farmers Union of Wales (FUW) on Monday evening.
The army said it hoped the training would go ahead, saying the majority of landowners had given their consent.
The military exercise is set to take place between 29 October and 6 November in north Carmarthenshire, Ceredigion and Powys and will involve up to 200 soldiers.
One of those who has refused permission for use of his land is Phillip Jones who farms around 100 acres at Crugybar near Llanwrda, Carmarthenshire.
He said: "It's not a personal thing against the soldiers and in the past my wife has provided them with tea and sandwiches.
"I understand that soldiers are professional people and need the tools to do a job but so do farmers and banning hunting has taken one of these tools away.
"We are surround by Forestry Commission land so it's difficult to flush the foxes out of the woodland - for farmers it is not sport it is a proven centuries old way of controlling foxes."
Mr Jones said some of his neighbours had also refused consent.
FUW County Executive Officer Peter Davies said members were being advised not to cooperate with the army.
"The military do wonderful work but farmers feel their backs are against a wall," he said.
"It is being done with a heavy heart but hopefully it will send a message to the government."
Colonel William Watson said the army regretted the decision.
"Within the UK the principle of your home is your castle is sacrosanct and we can only train on private land with the landowners' consent," he said.
"We remain indebted to those landowners who despite issues that they perceive as being detrimental to their way of life or the rural economy nevertheless continue to support our request for use of their land."