A Hampshire police spokesman said: 'We’re trying to identify two men who forced entry to the Spinnaker Tower, at about 9.15pm on March 9, before base jumping off the tower.
'It is alleged that the men caused criminal damage when they accessed the building.
'We’d like to speak to the two men, who put themselves in significant danger.'
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One man was white, in his 20s to early 30s, medium build, with bald or short cropped hair, and was wearing a light beige, long-sleeved t-shirt and light blue jeans.
The second man was also white in his mid-20s, had long, dark, scruffy hair with a full beard and with distinctive tattoos on both forearms.
He was wearing a red short-sleeved t-shirt and dark tracksuit bottoms.
Anyone who recognises the men, from the CCTV images or from the descriptions given, is asked to call 101 quoting 44170090193.