Stance detection is a critical component of rumour and fake news identification. It involves the extraction of the stance a particular author takes related to a given claim, both expressed in text. This paper investigates stance classification for Russian. It introduces a new dataset, RuStance, of Russian tweets and news comments from multiple sources, covering multiple stories, as well as text classification approaches to stance detection as benchmarks over this data in this language. As well as presenting this openly-available dataset, the first of its kind for Russian, the paper presents a baseline for stance prediction in the language.