Quote Originally Posted by zorro View Post
How about this? Это здание расположено на берегу озера Байкал. Is берег in the prepositional, озерo in the genitive and Байкал not declined?
Yes, you've got it right! "... on the shore of Lake Baikal" = "на берегу озера Байкал".
"На берегу" is in prepositional since it indicates a location (where?).
In "на берегу озера", "озеро" is in genitive, since it indicates a sort of "possession" (shore of the lake).

And "Байкал" is not declined when it follows "озеро":
Озеро Байкал - озера Байкал - озеру Байкал - озером Байкал - на озере Байкал.
Grammatically "Байкал" functions as an appostion here: Apposition - Wikipedia, the free encyclopedia.

Appositions in Russian usually do decline (из города Москвы), but sometimes they do not (из города Москва is also possible). Undeclinable apposition is mainly used when it is a geographical name or a title (like a name of a book, a newspaper, a film etc.).

Note if "озеро" is not used, "Байкал" would decline itself:
Байкал - Байкала - Байкалу - Байкалом - на Байкале.