Disclosed are compositions and methods for amplification of RNA molecules. The disclosed method involves synthesizing first strand cDNA molecules from RNA molecules, circularizing the first strand cDNA molecules and replicating the circularized first strand cDNA molecules using rolling circle replication. The method can be aided by the use of specialized primers for cDNA synthesis and specialized probes for circularizing the first strand cDNA molecules. The method can be used to replicate and amplify multiple RNA molecules, such as all RNA molecules in a sample or all mRNA molecules in a sample, or be used to replicate and amplify specific RNA molecules. Rolling circle replication of the circularized first strand cDNA molecules results in long DNA strands containing tandem repeats of the cDNA sequence. The tandem sequence DNA can be used directly (for detection of sequences, for example), further amplified, or used any other purpose. Double-stranded tandem sequence DNA can be used to produce unit lengths of the cDNA sequence. Tandem sequence DNA can also be transcribed to produce transcripts having sequence complementary to or matching the sequence of RNA molecules.