What would happen to a cruise ship if there was ever a major earthquake underwater?

The biggest danger caused by an earthquake under the ocean would be a tidal wave or tsunami. Like most waves, they increase in height and intensity as they move into shallower water, so it would depend on where the ship is at the time. In deep water, it would probably just ride out the swell, but if the ship were between the site of the earthquake and the shore, in relatively shallow water, it could be capsized by the wave.

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Shay, according to the Merriam-Webster Dictionary, a tidal wave can be triggered by an earthquake. It can be triggered by other causes, such as a storm or an incoming tide funneled into a narrow harbor, but nevertheless, tidal wave is a legitimate name for an earthquake-generated wave and in fact is listed as a synonym for tsunami in the dictionary:

Main Entry: tsu·na·mi
Pronunciation: \(t)su̇-ˈnä-mē\
Function: noun
Inflected Form(s): plural tsunamis also tsunami
Etymology: Japanese, from tsu harbor + nami wave
Date: 1897
: a great sea wave produced especially by submarine earth movement or volcanic eruption : tidal wave

Main Entry: tidal wave
Function: noun
Date: 1851
1: something overwhelming especially in quantity or volume a tidal wave of tourists
2 a: an unusually high sea wave that is triggered especially by an earthquake b: an unusual rise of water alongshore due to strong winds

This story might give an idea of what would happen. The ship was 20 miles from port when the tsunami hit. This happened on Dec. 26 after the Indonesian earthquake that created that devasting tsunami.

I think it really does matter on where the ship is in relationship to the earthquake epicenter and any subsequent tsunami created.

I read everyone’s answers but I don’t think a tsunami is the issue here. Underwater earthquakes or often due to volcanic activity and a large whirlpool might be formed toppling the ship.