Train from Venice to Florence and Train from Florence to Rome

Yes! Especially on the Venice to Florence section as you are crossing the country.

Between Bologna and Florence the train travels underground in a couple of tunnels that are 50 miles long in total. Fortunately the train will be traveling at almost 200 miles per hour therefore the experience lasts only about 20 minutes, but if you are afraid of the dark it will seem like a very long time. Between Florence and Rome there are also tunnels, but they are all short.

The history of railway tunnels through the Apennine mountains is a glorious one. The first Bologna-Firenze itinerary, through Pistoia, was very steep and had long tunnels, very dangerous with steam engines; huge airing fans had to be installed. A faster line was built in the thirties, with a 18.5 kms long tunnel that at the time was the third longest tunnel in the world. It had an underground station in the middle, that was actually used by commuters that began their day descending 1863 steps on a 27 degrees incline (about an hour needed), went to work to Bologna and had the same steps to climb when returning later in the day. Only a few minutes each year the sun matched in height the incline and the station had natural lighting.
The third itinerary, the new fast line, is built almost completely in tunnels; in most cases you have only a flash of light between adjoining tunnels, and there is just a longer stretch of open air railway crossing the Mugello valley. The first tunnel begins at the Bologna suburbs and the last one ends in a curve leading to Florence suburbs.

Tunnels between Florence and Rome look short in comparison, but there is a 10 kms one, a 7 kms, and several between 1 and 2 kms.