The Reaction Diffusion Master Equation (RDME) provides a stochastic framework for modeling spatially distributed biochemical systems. RDME is commonly analyzed using numerical simulations of trajectories over time, employing Monte Carlo methods, notably the Stochastic Simulation Algorithm (SSA), which incorporates potential randomness. However, the SSA is computationally demanding, and this grows worse when applied to largescale systems. In the present work, we use a parallel implementation to speed up RDME simulations. We leverage OpenMP with FORTRAN to effectively distribute calculations across several processors. This allows us to markedly decrease runtime while preserving accuracy, facilitating the simulation of time-consuming systems with the use of high-performance computing.