RNA function can be dictated by kinetics of folding and not simply by the nucleotide sequence or the structure of the lowest free energy state. In this report, we present a general computational approach to simulate the kinetics of RNA folding that can be used to extract population kinetics, folding rates and the folding of particular substructures or subsequences. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics of the maps are analyzed by solving the Master Equation on the map. We present results obtained using an analysis technique, Map-based Monte Carlo (MMC) simulation, that stochastically extracts folding pathways from the map. Our method compares favorably with other computational methods that begin with a comprehensive free energy landscape, illustrating that the smaller, approximate map captures the major features of the complete energy landscape. As a result, our method scales well to larger RNAs of more than 200 nucleotides. Our method predicts the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.