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In modern two-stroke SI engine applying one or two segments of catalytic converter in exhaust system is needed to fulfil requirements of emission of toxic components in burnt gases. In the paper dependence of location of catalytic converter with defined mass flow rate and resistance inside outflow system on engine performance, especially power and fuel consumption is described. Paper gives mathematical model of gas flow in a ‘tuned’ exhaust system with taking into account resistant of gas flow through catalytic converter. On the base of mathematical model calculation of physical parameter of gas for different location of monolith were done with overall engine output parameters. This enables optimisation of whole exhaust system at conservation of high temperature in the monolith. In the paper result of simulation (torque, fuel consumption, residual gas etc.) were given in comparison to original engine.