Extinction Rebellion said the protest was aimed at disrupting North Sea oil and gas operations.
The group said it activists, one of whom is from Dundee, “have assessed the risks and are properly prepared”.
On Monday afternoon, two of the group were seen making their way up one of the rig’s towers using climbing gear.
A third was spotted lower down.
Oil and Gas UK slammed the protest as a “dangerous and short-sighted stunt”.
According to Valaris’ latest fleet status report the 122 rig is scheduled to carry out a contract for Shell beginning on January 20.
Extinction Rebellion say its activists plan on remaining on the rig “as long as possible” in an effort to prevent it from returning to oil and gas operations.
The Dundee protester’s name was given only as Alison.
