We present a general computational approach to simulate RNA folding kinetics that can be used to extract population kinetics, folding rates and the formation of particular substructures that might be intermediates in the folding process. Simulating RNA folding kinetics can provide unique insight into RNA whose functions are dictated by folding kinetics and not always by nucleotide sequence or the structure of the lowest free energy state. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the Master Equation on the map. We present results obtained using an analysis technique, Map-based Monte Carlo (MMC) simulation, which 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 to larger RNAs. For example, in this paper we validate kinetics of RNA of more than 200 nucleotides. Our method accurately computes the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.