This paper presents a detailed physical model of an electro-pneumatic system, used to control Variable Geometry Turbochargers (VGT). The VGT actuator system consists of two parts, a diaphragm based pneumatic actuator and a solenoid based Electro-pneumatic Pressure Converter (EPC). The proposed model copes with the pressure dynamics inside the pneumatic actuator, with special focus on the EPC. The dynamics of both parts have been modeled separately and combined into one model by parameterizing the effective flow area and the air mass flow through the pneumatic actuator. The variations in volume, temperature and air mass flow rate have been taken into account. The model so obtained serves mainly for studying the effect of actuator dynamics on the global engine system. For control purposes, the detailed model is simplified to reduce the calculation load. Both models are validated using experimental data obtained from an engine test bench.