You can go by train from Stockholm to Narvik in Norway and then by bus from Narvik to Nordkapp. There is no train all the way.

Thanks You, and can you tell from where can then travel to Bergen?

To Bergen by train only via Oslo. Or taking a Bus that is not included in the Eurail Pass.

This bus in NOrge fra Narvik till Nordkappen is line 100 and it will take 2 days = you even need also to stay overnite at some point-the timetable differs a lot per season. BUSes in NO are very expensive for even west_Eur people. You can even get by bus-but again not in 1 day south fra Nordkappen till somewhere in FInland where you can continue by train again.

But what about reading a good guidebook en looking at a map before you ask all this?