GaN high electron mobility transistors (HEMTs) based on the III-V nitride material system have been under extensive investigation because of their superb performance as high power RF devices. Two dimensional electron gas(2-DEG) with charge density ten times higher than that of GaAs-based HEMT and mobility much higher than Si enables a low on-resistance required for RF devices. Self-heating issues with GaN HEMT and lack of understanding of various phenomena are hindering their widespread commercial development. There is a need to understand device operation by developing a model which could be used to optimize electrical and thermal characteristics of GaN HEMT design for high power and high frequency operation. In this thesis work a physical simulation model of AlGaN/GaN HEMT is developed using commercially available software ATLAS from SILVACO Int. based on the energy balance/hydrodynamic carrier transport equations. The model is calibrated against experimental data. Transfer and output characteristics are the key focus in the analysis along with saturation drain current. The resultant IV curves showed a close correspondence with experimental results. Various combinations of electron mobility, velocity saturation, momentum and energy relaxation times and gate work functions were attempted to improve IV curve correlation. Thermal effects were also investigated to get a better understanding on the role of self-heating effects on the electrical characteristics of GaN HEMTs. The temperature profiles across the device were observed. Hot spots were found along the channel in the gate-drain spacing. These preliminary results indicate that the thermal effects do have an impact on the electrical device characteristics at large biases even though the amount of self-heating is underestimated with respect to thermal particle-based simulations that solve the energy balance equations for acoustic and optical phonons as well (thus take proper account of the formation of the hot-spot). The decrease in drain current is due to decrease in saturation carrier velocity. The necessity of including hydrodynamic/energy balance transport models for accurate simulations is demonstrated. Possible ways for improving model accuracy are discussed in conjunction with future research.