The Transatlantic Tunnel is a structure proposed by one of the engineers involved in the construction of the Channel Tunnel beneath the English Channel.
It would be a tunnel that spans the Atlantic Ocean between New York City & London, England and could continue to Paris; the design calls for this tunnel to be raised above the ocean floor (making it a tube—not a tunnel); this is unlike most tunnels (which are dug out from beneath the floor of a water body), but like the Bay Area Rapid Transit system's Transbay Tube in San Francisco, the tunnel would be a 3,100 mile (5,000 km) long vacuum tube with mag-lev trains that could travel at speeds up to 5,000 mph (8,000 km/h).
At this speed, the travel time between New York and London would be less than one hour which would allow passengers literally to dine on one continent and eat dessert on another.
The tunnel would be held in place by using large tethering cables connected to the Atlantic floor by anchors which in some places would be almost five miles deep in an earthquake-prone zone.
The tunnel would be built using prefabricated sections which to be transported by a specialized ship called an immersion pontoon, then lowered into place. The sections would consist of a layer of steel surrounding a layer of foam surrounding another layer of steel.
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At top speed, the train would travel faster than a bullet fired from a ***. The train would be able to reach such a high speed as a result of the lack of friction and air resistance in this vacuum-sealed environment.
An alternative route that was proposed involved the train going from Newfoundland and heading north over the tundra of Greenland and across Iceland until it reached Scotland. This route is the cheapest but it is considered to be one of the most difficult due to the adverse weather conditions and rough terrain in Greenland, and such a tunnel would lose the vast speed of the mag-lev tube. It is estimated that once started, the project would take about 100+ years to complete.
The Transatlantic Tunnel is proposed to use a submerged floating tunnel which uses the same techniques as that of a submarine. The same idea is also being proposed for cars to use in crossing the fjords in Norway.
If ever built it would be the largest and most expensive construction project in history.
Source here and here