Police have released CCTV of two men who allegedly sprayed an oil-based substance onto the walls, floor and steps of the Anzac Memorial in Sydney 's Hyde Park yesterday.

Chief Inspector Gary Coffey said the "disgusting" vandalism to the heritage-listed site would cost up to $20,000 to remove.

The two middle-aged men allegedly responsible can be seen on the footage moving casually around the site, appearing to spray a substance onto the walls, steps and floor.

Coffey said the men were at the memorial for 20 minutes and at one point even engaged with staff.

The men then left the memorial together and walked north through Hyde Park.

Cleaners are at the site today, attempting to remove the oil-based substance, which Coffey said had caused "permanent" staining to the granite.

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