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A detailed mathematical model of the thermodynamic events of a crankcase scavenged, two-stroke, SI engine is described. The engine is divided into three thermodynamic systems: the cylinder gases, the crankcase gases, and the inlet system gases. Energy balances, mass continuity equations, the ideal gas law, and thermodynamic property relationships are combined to give a set of coupled ordinary differential equations which describe the thermodynamic states encountered by the systems of the engine during one cycle of operation. A computer program is used to integrate the equations, starting with estimated initial thermodynamic conditions and estimated metal surface temperatures. The program iterates the cycle, adjusting the initial estimates, until the final conditions agree with the beginning conditions, that is, until a cycle results.