The high-risk activity, involving people jumping from cliffs, walls and piers into water for fun, has led to people being left paralysed, or even dead, after leaping into the unknown waters below.
More than half those involved in tombstoning are teenagers, a quarter are in their 20s, and the majority are either boys or men.
Sussex Police Inspector Gareth Davies said: “Tombstoning is an extremely dangerous practice and we cannot advise strongly enough against it.
“It is very hard to judge the depth of water due to swell and sea conditions and to see any objects lurking below the surface.
“Serious injuries, sometimes resulting in death, are often sustained from hitting the seabed or an underwater obstruction.
“It’s not worth ruining your life for a dare or a quick thrill.”
A Maritime and Coastguard Agency spokesman said: “Jumping into deceptively shallow water is not the only danger posed by tombstoning.
“The shock of cold water can make it difficult to swim and strong currents can rapidly sweep people away.
“Think before you jump.
“Don’t let alcohol, drugs or peer pressure affect your judgement.
“Even if you are jumping safely, children may be watching and copy your actions.
“Since 2007, nationally, there have been at least 14 deaths and 40 serious injuries due to tombstoning.
“Don’t jump into the unknown.”