A Godalming memorial is in danger of collapse if a spate of vandalism continues, according to Surrey Police.
Three large supporting stones were loosened and removed from the Phillips Memorial Cloister on 2 December.
Between 10 and 15 cobble stones were also stolen from under the pillars of the cloister between 1400 GMT on 29 November and 1400 GMT on 30 November.
Surrey Police have been carrying out extra patrols in the Phillips Memorial Park since the thefts.
Pc Derek Fry said: "We are doing all we can, not only to prevent further offences being committed in the area, but also to bring those responsible to justice.
"The safer neighbourhood team have been joined by colleagues from the dogs unit and targeted patrol team in carrying out regular patrols in the area."
The 1914 memorial to Jack Phillips, chief telegraphist on the Titanic, is said to be one of the largest of any built to remember a single Titanic victim.
Mr Phillips was born locally and died aged 25 when the liner sank.
Pc Fry said: "The Phillips Memorial Cloister was built as a testament to a local hero who gave his life to try and save others and should be an area that people of the town can be proud of.
"It is disappointing the depths that some people will sink to for their own amusement or profit."