The popularity of the event means thousands will miss out on May 14 because there is only a capacity for 7,000 visitors.
About 20,000 people have pre-registered to purchase tickets for the chance to walk the length of the 1.2 mile tunnel underneath the Devil’s Punchbowl.
Tickets officially go on sale at 10am on Wednesday and are available on a first come first served basis.
They are priced at £6 for adults, £3 for children, and cover the cost of parking and the coach ride to and from the tunnel and the park and ride car parks.
Hindhead Together project co-ordinator Caroline White said: “Obviously a lot of people are interested in the project itself – it is the longest under land tunnel in the country and it has been decades in the making.
“People are very keen to get a first glance at it from the inside after having seen it from the outside for so long. They want to see what it looks like up close.”
She added the public were fascinated by the construction and engineering work as well.