Abstract: RNA polymerases are enzymes that transcribe genes from DNA onto strands of RNA. The transcription elongation by multisubunit RNA polymerases is processive but nonuniform: one enzyme can translocate along the DNA template for thousands of nucleotide addition steps but, sometimes, it can enter backtracking long pauses. Here, we present a Brownian ratchet model for the processive transcription elongation and the backtracking long pauses, which is developed based on the available structural and biochemical studies. Using the model, we analytically study the dynamics of the transcription elongation, such as the effects of external force and NTP concentration on the transcription velocity free of pauses, and the dynamics of backtracking long pauses, such as the probabilities of entering and returning from the backtracking pauses, with the analytical results in good agreement with the available single molecule experimental data. Values of several parameters for both Escherichia coli and Saccharomyces cerevisiae RNA polymerases such as their affinities for the DNA/RNA substrate during transcription elongation are determined. Moreover, some testable predictions are presented.