I'm assuming you are asking about a tunnel between North America and Europe.
There are two types of tunnel that "might" be possible: excavating a tunnel through the rock beneath the sea bed or sinking prefabricated sections of tunnel to the sea floor, joining them up and sealing them against water inflow.
Problem #1 - Depth of the North Atlantic Ocean
The depth of the Atlantic Ocean is between 3700 and 5500 metres. Such depths are going to make it extremely difficult to sink the tunnel sections, assemble them, ensure they can survive the water pressure and be water tight.
Additionally, such deep water will increase the ground stresses in the rock in the sea bed, which will be problematic for an excavated tunnel.
Problem #2 - Geological Reconnaissance
For an excavated tunnel, the sea bed will need to drilled along the proposed path of the tunnel at closely spaced intervals so core sample can be taken, so that geologists can determine what type are rock or soil (sediments) are there and ascertain material properties for the rock. They will also need to know what geological structural discontinuities are present, such as faults, where they are located, how they are orientated and how adverse they could be.
Drilling in waters 5500 metres presents a whole lot of challenges, one of them being the drill string would be unsupported for the first 5500 metres of its length.
Geological reconnaissance would also be required for a sunk tunnel to ensure the sea bed could support the weight of the tunnel sections. Having sections of tunnel subside into soft sediments is something that would need to be prevented.
Problem #3 - Ventilation
Ventilation shafts rising though 5500 m of water would be problematic in terms of construction, support and possible impact by whales, ships or submarines. They would also need to be water tight to prevent water inundation of the tunnel.
The only way to ventilate such a tunnel would be via ventilation tunnels parallel to the main tunnel. These could double-up as service tunnels for inspections, maintenance and rescue, should there be a fire in the main tunnel.
For reasons of safety, ventilation tunnels would need to be duplicated, at least.
Ventilation fans would need to be placed at the ends of the vent tunnels. They would need to be large and they would consume a lot of electricity.
Problem #4 - Traversing an Active Volcanic Zone
There is an entity called the Mid Atlantic Ridge. This is an active volcanic zone that is pushing apart the continental plates that separate the Americas from Europe and Africa. This ridge is visible above the water on Iceland.
Putting a tunnel on or through the Mid Atlantic Ridge may not be possible. If it were possible, the tunnel would require regular maintenance to remedy damage done by the Ridge.
Putting ventilation tunnels through the Mid Atlantic Ridge would be give additional ventilation problems.
The distance between Canada and Ireland is close enough to 3000 km.
The cost of construction a trans Atlantic tunnel would be hideously expensive!