We have developed a software system called SIMISYS that models and simulates aspects of the human immune system based on the computational framework of cellular automata. We model tens of thousands of cells as exemplars of the significant players in the functioning of the immune system, and simulate normal and simple disease situations by interpreting interactions among the cells. SIMISYS 0.3, the current version, models and simulates the innate and adaptive components of the immune system. The specific players we model are the macrophages, dendritic cells, neutrophils, natural killer cells, B cells, T helper cells, complement proteins and pathogenic bacteria.