Suomen Kansan Vanhat Runot (Old Poems of the Finnish People) is a collection of nearly 90,000 oral folk poems written down between 1564 and the early 20th century. It is characterized by frequent reoccurrence of similar pieces of text on various levels (from entire poems, through passages to single verses and collocations). However, finding these similarities is challenging due to a high degree of orthographical, morphological, and compositional variation. In this article, we propose a method for automatically identifying equivalent verses, i.e. verses conveying the same meaning with the same words, using a clustering based on cosine similarity of character bigram vectors. The method achieves around 81% F-score and has been successfully used for identifying similarities across the entire SKVR corpus on the level of verse, passage, and poem. The results can be browsed through a Web interface.