This paper presents experimental results and a new computational model that investigates Cycle to Cycle Variations (CCVs) in a Spark Ignition (SI) engine. An established Stochastic Reactor Model (SRM) previously used to examine Homogeneous Charge Compression Ignition (HCCI) combustion has been extended by spark initiation, flame propagation and flame termination sub-models in order to simulate combustion in SI engines. The model contains a detailed chemical mechanism but relatively short computation times are achieved. The model is validated by simulating the pressure profile and emissions from an iso-octane fuelled single cylinder research engine that showed low CCVs. Experimental results that show cycle to cycle fluctuations in a four-cylinder naturally aspirated gasoline fuelled SI engine are presented. The model is then coupled with GT-Power, a one-dimensional engine simulation tool, which is used to simulate the breathing events during a multi-cycle simulation. This allows investigation of the cyclic fluctuations in peak pressure. It is then demonstrated why the detailed exhaust composition obtained may be necessary to simulate the transition between SI-HCCI-SI engine operating modes in future work.