The phenomenon of drop deformation and breakup in simple shear flow due to its great impact on determination of drop size in emulsions, is of utmost significance. Various numerical and experimental methods can be used to study this phenomenon. The dissipative particle dynamics method was selected as an appropriate method for solving this problem due to its acceptable accuracy and reasonable computational cost as well as the fact that it does not require to locate the interface. To familiarize the reader with this method, a relatively comprehensive description is presented on using the dissipative particle dynamics method for simulating fluid mechanics problems. After this introduction, the problem of steady state deformation of a drop in simple shear flow is investigated for further familiarity with the phenomenon of drop deformation and breakup and identifying the factors influencing it. For this purpose, the final drop shape and its orientation were calculated for different capillary numbers and the results were compared with those obtained from other numerical methods as well as analytical relations. These comparisons showed that the applied numerical method had acceptable accuracy. The effects of the drop distance from the wall, the viscosity ratio, and the inertia on the drop deformation and breakup were also investigated. Through simulation, the similarity between the behavior exhibited by the drop and that exhibited by a mass-spring-damper system was demonstrated. In Stokes flow, the drop behavior resembles that of an over damped system and at high Reynolds numbers, the drop behavior is similar to that of an under damped system. This study also simulated the phenomenon of drop breakup in simple shear flow under critical and super critical conditions for the purpose of studying the effective factors on the final size of the dro resulting from breakup. Three factors were studied: shear rate of the flow, the initial drop size, and the viscosity ratio. It was observed that increasing shear rate led to the decrease of the final drop size. The relation between shear rate and final drop size for different Reynolds numbers was expressed as an exponential function with exponents 1.0 and 0.66 for the Stokes flow and inviscid flow respectively. Since the Reynolds numbers experienced by the drops are average values, the exponent in this study was calculated as 0.74. Also, it was shown that the mean drop size was proportional to the critical drop size. This result is in good agreement with experimental results. Upon investigating the effect of the initial drop size on the mean size of the drops, it was revealed that this had no effect on the final size obtained for the drops. Large viscosity ratios led to instabilities with large wavelengths as well as throat-shaped regions with more volume. This caused the satellite drops to become larger in this case and two major modes were distinguished for the drop size distribution. Based on the results obtained for producing monodisperse emulsions, the first step would be to prepare a pre-mixed mixture with different drop sizes greater than the critical size. Then, the final size of the drops can be controlled via applying a shear flow. Also, to prevent an emulsion with wide drop size distribution, fluids with viscosity ratios less than unity must be used for both the drops and their surrounding fluid. Keywords: Emulsion, Drop Breakup, Simple Shear Flow, Dissipative Particle Dynamics, End- Pinching, Capillary Instability, Drop Size Distribution