The exhaust gas recirculation (EGR) is widely used to reduce NOx emissions in diesel engines. However an excessive EGR rate in the cylinders leads to reduction of NOx and increment of particulate matter (PM) or misfire. In order to overcome this problem, the EGR mass flow rate should be controlled precisely. To control the EGR mass flow rate accurately, the EGR mass flow rate should be estimated correctly. This paper presents a physics based model of Variable Geometry Turbocharged diesel engine to estimate EGR mass flow rate. The diesel engine model includes subsystems of intake manifold model, exhaust manifold model, variable geometry turbocharger model, effective area for EGR valve model and exhaust gas temperature model. Models of the individual subsystem are implemented in MATLABTM/SIMULINKTM environment. These models are coupled together to form overall model for EGR mass flow rate estimation for variable geometry turbocharged diesel engine. Experimental data available from testing is used for simulation. Most of model is based on fundamental laws of physics and hence generic. The overall model has five inputs i.e. engine speed, fuel supply rate, intake manifold temperature, percentage VGT opening and EGR valve opening. The output of model is EGR mass flow rate and EGR ratio. Typical step input is provided to the engine model to study effects on output variables. The model is simulated for transient engine operating condition by sudden increasing or decreasing engine speed at different loading conditions. The estimated EGR mass flow rate and EGR ratio are found to be in acceptable range.