Published Tuesday, 22 April 2014
Headstones were damaged and graffiti scrawled on monuments in the attack. (© UTV)
One headstone has been smashed and 13 more have been damaged in an area of the cemetery for those who died in World War 1 and World War 2.
Police also said a Cross of Sacrifice war memorial has been extensively covered in graffiti.
In a statement the Royal British Legion in Ireland said: "The Legion is saddened to hear of this senseless incident. War memorials and graves honour the memory of service people who have made the ultimate sacrifice and those who defend the freedom we enjoy."
It is believed the attacks at the Falls Road cemetery were carried out at some stage between 15 and 22 April and anyone who witnessed suspicious activity over the past week is asked to call the PSNI.
Information can be passed on via the non-emergency number 101.
© UTV News