UPDATE: Two 17-year-old boys have handed themselves into Albury police after the incident.
The boys told police they were the pair depicted in the Snapchat images urinating on the war memorial.
They handed themselves in to police after The Border Mail published the image.
The incident occurred about 3am on Thursday.
EARLIER: A Snapchat image of what appears to be two people urinating on Monument Hill has left Albury's Council and RSL representatives angry.
The photograph, taken from behind the culprits, shows two males facing the structure.
The wording reads “taking a piss on monument”.
Albury RSL sub-branch president Graham Docksey was left shaking his head at the low act.
“I think it's most disappointing that these things are still happening,” he said.
“With some good luck, we'll be able to identify these people and publicly shame them.”
Albury Council has CCTV cameras positioned at the monument after previous vandalism attacks.
There are people who do get hurt by those sort of actions.
The structure was built using money raised by the public, to remember soldiers who died in World War I.
“It's a major tourist attraction to Albury, but more important than that, it's a memorial to our soldiers,” Mr Docksey said.
Albury RSL sub-branch vice president Mark Dando said many people who served overseas would be saddened.
“To the young people involved – please have a think before you go and do stupid things like that,” he said.
“There are people who do get hurt by those sort of actions.
“We go into schools and talk about not just Anzac Day, but the Anzacs in general and the different battles Australians have been involved in.
“Those kids I've spoken to would be pretty disgusted.
“They hold our defence forces with pride.”
Mr Dando wants to see those responsible named and shamed.
“They should be given a pressure washer and some cloth to clean up any mess they cause.
“This is not the first time.
“About 18 months or two years ago we had some head stones knocked over at the war cemetery.
“Maybe I'm getting too old, but I just don't get it.
“I can't believe that people would desecrate those sorts of places and the memories of those who have done nothing but given their lives to look after them.”
Police Inspector Gary Lewis said he hoped it wasn't a deliberate act.
“This is clearly an act that anyone who understands the significance of the memorial and the sacrifices made by those who it pays tribute to would find extremely offensive,” he said.
“You would like to think this was an error of judgement by those involved rather than a deliberate act of disrespect.
“I would urge anyone with information about the incident to contact Albury police."
Call (02) 6023 9299.