Tunnels by train between Vienna and Budapest?

None that i can recall.

East of Vienna the great Hungarian plain commences. There are no mountains between Vienna and Budapest. There are no tunnels along this train route.

West of Budapest and east of Vienna and extending from central Budapest up into Slovakia are the hills of Buda, and further east the foothills of the Carpathian Mountains do touch on Hungary, so tunnels do exist. Hungary has 21 rail tunnels. The longest is 0.78km and is located just outside of Budapest between Budapest and Vienna, but not on the line that serves Vienna. Currently another tunnel, number 22, is in the environmental impact planning stages. It will be 4.5km long and will run under the Danube and connect Nyugati station to Kelenföld Station. That would allow trains from Vienna to serve both Keleti Station and Nyugati Station.

If you plan a daytrip to Szentendre (wonderful little town, worth the 45 minute ride), the H5 commuter train makes part of the journey underground. About 10 minutes worth. But I can direct you to the first stop above ground if you would like

Then there is the issue with the metro system. All underground with a brief exception of the last 2 stops at the eastern end of the M2 line. Maybe crossing under the Danube on the M2 or M4 metro will make you especially nervous. To be honest, doesn’t light my fire either. https://justbudapest.com/wp-content/uploads/Budapest_metro-992x816.png. But there are above ground tram routes that will take you to every place the metro does for tourism.

If tunnels bother you, you might want to avoid the automotive Buda Castle Tunnel. Built in 1857 its .35km long. It connects the Chain Bridge with Buda by going under Castle Hill.

Then there are the trams. The 2/2B/23 Tram dips down under the Chain Bridge, but that’s quickly done. But then a bit further down stream it goes to a fairly large underground stop at the Fővám tér metro station located under the Liberty Bridge (Szabadság Bridge).

If you are taking the train from Vienna to Budapest, you will arrive at Keleti Station unless you ride the private Regiojet line. If you dont want to go underground you will need to use a taxi or a bus to your accommodation. Otherwise Keleti is served by the M2 and the M4 underground metro. But we can find a Plan B.

If you want to use a taxi I like CityTaxi and they have a good app. Always better to "call" one on the app than do one at the curb. For the bus, when you have accommodations let me know and I can help. The stops are scattered around the station. Generally to most hotels in Pest the best route involves a short run on the M2 metro line.