A method of inhibiting replication of a flavivirus in animal cells, and an oligonucleotide compound for use in the method are disclosed. The oligonucleotide analog (i) has a nuclease-resistant backbone, (ii) is capable of uptake by the cells, (iii) contains between 8-40 nucleotide bases, and (iv) has a sequence of at least 8 bases complementary to a region of the virus' positive strand RNA genome that includes at least a portion of SEQ ID NOS:1-4. Exposure of cells infected with a flavivirus to the analog is effective to form within the cells, a heteroduplex structure composed of the virus ssRNA and the oligonucleotide, characterized by a Tm of dissociation of at least 45° C., and having disrupted base pairing between the virus's 5′ and 3′ cyclization sequences.