Modeling a polity based on viable scientific concepts and theoretical understanding has been a challenge in computational social science and social simulation in general and political science in particular. This paper presents a computational model of a polity (political system) in progressive versions from simple to more realistic. The model, called SimPol to highlight the fundamental structures and processes of politics in a generic society, is developed using the combined methodologies of object-based modeling (OOM), the Unified Modeling Language (UML), and the methodology of Lakatos’ research programs. SimPol demonstrates that computational models of entire political systems are methodologically feasible and scientifically viable; they can also build on and progress beyond previous theory and research to advance our understanding of how polities operate across a variety of domains (simple vs. complex) and levels of analysis (local, national, international). Both simple and realistic models are necessary, for theoretical and empirical purposes, respectively.