There's trains from Sochi to Mineralnye Vody, but they are more likely to set you back around 50 euro's - if you don't get in trouble. Honestly, if you can't spare 117 euro's, you've got bigger issues ;).

Why dont you go by car? If you are 4 people splitting the petrol cost and you depart from Bulgaria, I belive it will be pretty cheap.

In 2007 me and some friends drove from Stockholm to Elbrus via the Baltics, Poland, Ukraine and ferry between Kerch - Port Kavkaz. It was a lot cheaper option than go by air via Moscow. And the petrol gor cheaper and cheaper the closer we got to Elbrus..

Well, it would probably been cheaper/faster to go directly by car via Rostov-on-don, but we wanted to have some slack days on the crimean beaches before entering Russia. Plus we had some spare days before our visas got valid, drove faster than planned...

There was railways in Kerch, but if they were used for public purpose our industry I do not know.

Not a single bribe or police hustle on the whole trip, I believe our strange appearance (4 bearded hobos in a rustly old golf with all luggage tied on the roof) might have had an impact on this!

We met a gang from a serbian alpine club who hade drove from Beograd in a new fancy mini van, they had alot of trouble on the way and had to pay bribes, etc. If you speak russian, keep low profile and sound like a dumb tourist even though you understand what they are saying. To be able to take our swedish registered car into Russia we bought a car insurance from an office in the harbour of Kerch (next to the ferry). It was pretty cheap, dont remember exactly how much it was, but it was cheap...