Motivation: The Flavivirus genus includes several important pathogens, such as Zika, dengue and yellow fever virus. Flavivirus RNA genomes contain a number of functionally important structures in their 3′ untranslated regions (3′UTRs). Due to the diversity of sequences and topologies of these structures, their identification is often difficult. In contrast, predictions of such structures are important for understanding of flavivirus replication cycles and development of antiviral strategies. Results: We have developed an algorithm for structured pattern search in RNA sequences, including secondary structures, pseudoknots and triple base interactions. Using the data on known conserved flavivirus 3′UTR structures, we constructed structural descriptors which covered the diversity of patterns in these motifs. The descriptors and the search algorithm were used for the construction of a database of flavivirus 3′UTR structures. Validating this approach, we identified a number of domains matching a general pattern of exoribonuclease Xrn1-resistant RNAs in the growing group of insect-specific flaviviruses.