But authorities are trying to stop them because they fear someone will fall.
The tunnels are also on restricted Lyttelton Port Company land.
A number of urban explorers have been caught trying to access and coming out of the tunnels, a port spokesperson said.
The port has called the police in some instances, who have taken details and issued two trespass notices.
"Anyone who enters is potentially committing an offence," the port spokesperson said.
"The land is also very steep and dangerous to climb and creates a risk to those attempting to enter."
Urbex members made an impact by going into the earthquake-damaged Christ Church Cathedral in 2014, sparking outrage with photos showing the deteriorating building’s interior.
The groups have also visited derelict film sets and Ripapa Island on Lyttelton Harbour when it was closed in 2016. They took photos at the island’s heritage sites, the pā, a quarantine station and a prison.
The people going into the caves below Sumner Rd have posted a video on TikTok.
The TikTok, titled Lyttelton’s Underworld, was posted on June 29 where a person explores the tunnel. When the person emerges, a LPC security van is waiting for them.
Social media posts have encouraged more people to enter the closed tunnel system over the past three months, the port spokesperson said.
Police and Customs officials have increased patrols on Sumner Rd to try and stop the urban explorers.
Customs monitor the port as it is a customs-controlled area.
LPC is considering other methods to prevent people from entering the tunnels and cliffs.
"Additional options to deter behaviour include putting up higher fences and posting warning signs not to enter," said the spokesperson.
The tunnels were used to store oil if the Allies had to move ships and other naval assets away from the Japanese advance.
By September 1944, construction of the tunnel system stopped when it was clear the Allies were winning in the Pacific.
The tunnel system has been blocked off since the Maritime Security Act was passed in 2004 to stop the public from accessing it for security reasons.