GillespieSSA is a package for the statistical computing and graphics language and environment R. GillespieSSA provides a simple to use and extensible interface to several stochastic simulation algorithms for generating simulated trajectories of finite population continuous-time model. Currently it implements Gillespie’s exact stochastic simulation algorithm (Direct method) and several approximate methods (Explicit tau-leap, Binomial tau-leap, and Optimized tau-leap). The package also contains a library of template models that can be run as demo models and can easily be customized and extended. Currently the following models are included, decaying-dimerization reaction set, linear chain system, logistic growth model, Lotka predator-prey model, Rosenzweig-MacArthur predator-prey model, Kermack-McKendrick SIR model, and a metapopulation SIRS model.