Postmen are being told by managers to walk faster to complete their rounds quicker, a union has claimed.
The Communication Workers Union (CWU) said that a new software system, Pegasus - which calculates the optimum post load that can be delivered by staff - is being used, requiring delivery staff to walk at four miles an hour.
Bob Gibson, CWU national official, said: "Royal Mail is using this system to meet financial savings without considering the physical realities of delivery rounds. This is putting pressure on delivery workers and leading to bullying and harassment.
"CWU has an agreement with Royal Mail to jointly review all aspects of Pegasus, but the business has reneged on this and is pushing ahead with damaging changes without input from the union."
A spokesman for Royal Mail told the BBC the claims were "nonsense", and that it wanted delivery workers to walk at an average of 2.1 miles per hour.
"Royal Mail would never ask or require postmen and women to do anything they are not capable of performing," he said. "It is simply nonsense to suggest that we require anyone to deliver the mail at an average walking speed of more than four miles an hour."
The organisation would take action to deal with any harassment or bullying that took place, he added.