North Wales Police said the attack appeared to be random
More than 30 gravestones in a churchyard have been smashed and pushed over by vandals.
Some of the damaged stones at St Trillo's Church in Rhos-on-Sea, Conwy date back to World War I.
North Wales Police described the attack as "mindless hooliganism" and appealed for witnesses to come forward.
Conwy councillor Phil Edwards said there had been previous problems with children drinking alcohol in the churchyard but this had been stopped.
The churchyard is the final resting place of Harold Lowe, the officer on the Titanic who saved four passengers from the doomed liner in his lifeboat in 1912.
His grave was not vandalised but the tombstone of Adela Wylie, who died in 1914, has been pushed forward and its cross broken.
The cross on Ralph Ogden's tombstone, who died in 1918, has also been smashed.
Coun Edwards said the vandalism was "enough to turn your stomach".
"It is terrible to see these smart imposing grave stones pushed over," he said.
"If it was children that did this, they must have been older children, and there must have been more than one, because these stones were big and heavy.
"There have been problems in the past with children using the church yard to drink (alcohol), but that had been stopped.
"This is truly awful. And if there are any family members still alive they must be very upset."