Lincoln Dodd and 6ft 2in Barry Sele are suing Sun Valley Foods, claiming sex discrimination because they were turned down for jobs because of their height.
The pair, who have both worked for the poultry and meatpacking firm in the past, said that the height restriction discriminated against men because women are, on average, shorter.
Mr Dodd, 27, told an industrial tribunal in Hereford that the rejection for the job last December had "devastated" him.
Mr Sele, 21, said he could not understand it when the company nurse carrying out a pre-employment medical told him his height meant he had no chance of a job.
"The nurse asked me how tall I was and I said 6ft 2in, and she said there was no job for me because I was too tall," he said. "I was really amazed. She said they had just brought in new guidelines saying they were not allowing people of a certain height.
"I was not measured apart from my overall height and then she just asked me if I wanted to be walked off the premises."
The company, which makes processed meals for Tesco, McDonald's and other leading retailers, said the two men were not turned away because of their height, but because their "very long spines" - in relation to their thigh bones - made them more likely to suffer from back injuries while working on the production line.
The tribunal heard that Sun Valley automatically rejected all applicants over 6ft 5in and referred people between 6ft 3in and 6ft 5in to its occupational health centre.
Before the hearing a spokesman said the company was merely acting in a responsible manner in avoiding injury to employees.
"If you are more than 6ft 5in, it is likely you are so tall that you will damage yourself doing the job," he said.
Outside the tribunal, Mr Dodd said that his height had been a real problem when he was growing up.
"When I was 11 or 12 I even asked my mum and dad if I could have an operation to stop me growing," he said.
"My mum said I would be glad when I was older. But when I was turned down for the Sun Valley job it brought back all those childhood psychological problems."
Both men told the hearing that they had previously worked for the Hereford plant without any difficulties. Mr Dodd's previous job involved mixing, weighing and loading chicken and other meats in preparation for the production line.
Phil Heinricy, founder of the Tall Persons' Club of Great Britain and Ireland, said that applying any form of height criteria would automatically adversely affect men.
"Men would be rejected at height levels to a much greater extent - perhaps 40 to 80 times as many men would be rejected as women," said the 6ft 8in Mr Heinricy.
The most recent health department statistics show that 12 per cent of men and 0.1 per cent of women are over 6ft.Reuse content