Abstarct: Nowadays, for reaching the new oil and gas reservoirs underneath the earth and oceans, drilling of directional, horizontal, ERW and multilateral wells are common. With the increment of well’s depth and inclination, hole cleaning becomes severe and the safe mud window becomes narrower. These difficulties cause various problems such as pipe sticking, hole pack off, fluid loss and etc. which will cause well loss or a waste of money if we do not manage and control it properly. Drilling hydraulics optimization is the best tool for preventing and controlling this kind of problems. Due to what have been mentioned regarding hole cleaning and ECD in modern drilling, the necessity of drilling hydraulics optimization and the ECD is an obvious fact. In this method of optimization, we are looking for the specific flow rate and nozzle size (with the consideration of practical limitations) in which the hole cleaning and well stability (ECD and staying in the safe mud window) is been guaranteed. For this process of optimization, it is necessary to calculate the precise pressure drop and hole cleaning condition in which the rheological model used is playing a prominent role. In this thesis, firstly, in order to find the best rheological model for predicting rheological properties and pressure drop of the fluid, seven common rheological model in drilling industry such as Bingham-Plastic, Power-law, API, Herschel-Bulkley, Casson, Robertson-Stiff, and Sisko had been investigated. The results show that the Casson model is the best one for pressure drop calculations. For the investigation of hole cleaning, by combining three analytic-experimental models of the Dispersed model, Modified Larsen and Rubidiani a comprehensive approach for predicting the minimum required flow rate for carrying the cuttings had been recommended in which the results show the excellency of the precision of this model in comparison with other analytical-experimental models. After that, for optimizing the drilling hydraulics, with considering proper hole cleaning and ECD, the annular hydraulics window and bit hydraulics optimization windows had been employed. Finally, the recommended approach for optimization had been used for drilling hydraulics optimization in the wells of an offshore jacket located in the Southern-Pars field.