I'm not a native speaker of Russian myself, so I looked it up in Ladefoged & Maddieson (1996): "The Sounds of the World's Languages," where it says that the Russian r is an alveolar trill. However, it is a bit different from the Spanish one. According the analysis of Russian by Ladefoged & Maddieson, the Russian alveolar trill is apical, which means it is pronounced with the tip of the tongue, and it only consists of two flaps - and sometimes only one, in which case it would be considered an alveolar flap. The Spanish alveolar trill on the other hand is laminal, which means it is pronounced with the tongue blade, and it normally consists of two or three flaps, and never one (to distinguish it from the Spanish alveolar flap, and create minimal pairs such as pero vs. perro and caro vs. carro).
Thank you. I can't imagine a laminal trill. Have you ever heard Russian? What was your impression about this issue?