Chapter one discusses the drilling fluids, its functions, types and composition of water based, oil based and synthetic based mud systems. Chapter two lays solid emphasis on drilling fluid flow behaviour pattern such as laminar, transient and turbulent flow regimes. The Newtonian and various non-Newtonian fluids were also discussed. Chapter three addresses various rheological model parameters of drilling fluid as well as different methods of rheological parameters measurement. While chapter four dealt with various rheological models of drilling fluid. Chapter five analyzed the various drilling fluid rheological models discussed in chapter four and used the results of laboratory experiment to select the most appropriate rheological model for drilling fluids. Chapter six explains how the errors associated with Bingham Plastic rheological model at low and high shear rate conditions can be mitigated by development of a modified Bingham plastic model with dimensionless stress correction factor. Finally, chapter seven discusses the various uncertainties associated with various rheological models in pressure losses estimation during drilling operations and how they can be addressed.