Smart phone game Pokemon Go guides those taking part to real-life locations where they can fight each other’s captured creatures, with Annan War Memorial in the town’s High Street chosen as one of these sites.
But Royal Burgh of Annan Community Council vice-chairman Neil McIntyre said: “I think it’s disgraceful – that’s my personal view.
“It’s very inappropriate.”
Pokemon Go launched in the UK last week.
Players who download the smart phone app are encouraged to find creatures called Pokemon.
The game uses the player’s real-life location to generate a map.
Players with captured pokemon are then encouraged to pit them against each other at locations called ‘gyms’.
Globally, there has been controversy over players hunting pokemon in graveyards, at Auschwitz, in the Holocaust museum at Washington DC, and at the 9/11 memorial in New York.
Voicing concerns, Mr McIntyre said: “The other night they walked into The Blue Bell pub.
“One of the part-time bar staff said they came in and said, ‘There’s Pokemon in the Blue Bell’.
“But that’s inappropriate – it’s encouraging youngsters to go into public houses.”
However, concerned most about the use of the war memorial as a location which players are encouraged to battle for possession, the military veteran said: “They should have given it a heck of a lot more thought.”
Dumfries and Galloway Council’s Armed Forces Champion Archie Dryburgh acknowledges the sensitivities, but points to the distinction between fantasy and reality.
Councillor Dryburgh said: “There’s a big difference between the virtual world and the real world.
“Obviously, choosing a war memorial in Annan may not have been the best in taste, but at the end of the day it’s a virtual world where people are maybe having some fun and you don’t want to stop people having some fun.
“But it might be a bit of bad taste to have it at the Annan War Memorial. I’m presuming that whoever put it there didn’t come from Scotland, or from Annan, and just chose a place on a map.”
Pokemon Go company Niantic have yet to respond to the criticism.