Amphiphilic surfactants are important components in many applications such as the detergents, cleaning agents, emulsifiers in food, pharmaceuticals, cosmetics and also drag reduction. Whereas a shear flow applied on a surfactant solution influences the self-assembled structure of surfactant molecules, understanding the shear effects on the surfactant molecular assemblies is of importance. This great interest is being reflected in the large number of experimental and theoretical studies. The study of these self-assembling systems however, is quite challenging because of the different length scales and the associated different times scales involved in the problem which implies large system sizes and long simulations. Therefore, we need a multi-scale scheme that spans the required length and time scales, at the same time preserving the important aspects of the atomistic model. The goal of this thesis is to investigate the behavior of surfactant under shear flow by dissipative particle dynamics. Dissipative particle dynamics (DPD) is an emerging method for simulating problems at mesoscopic time and length scale. Studying the DPD methodology based on dimensionless numbers and expressing its scales in terms of physical units can open ways to understand the physical behavior of the system and to model practical problems. In the DPD method the surfactant is modeled using particles, which connected by harmonic springs. Self assembly of surfactant molecules is investigated to form a wide range of structures such as spheres, cylinders, bilayers and double bilayers. Then Shear flow is applied on a surfactant solution by means of Lees–Edwards boundary conditions. The rheological behavior of surfactant such as the morphology of micelles, the shear rate dependence of shear viscosity of the micellar solution and viscoelasticity of solution in different concentrations solutions and different shear rates are examined. The results has been shown that the first shear thickening at low shear rate is accrued, which is caused by the growth of spherical micelles, while the consequent shear thinning for higher shear rates is caused by orientation of micelles by increasing the shear rate. Results showed the stretching of spherical micelles in the flow direction under shear flow and the occurring a microstructural transition in high shear rates from spherical to rod-like structure. We also measured the first and second normal stress difference. The results show that the first normal stress difference increases as shear rate raises, whereas the second normal stress difference (N2) is almost zero. The first normal stress difference is increased as concentration increased because of viscoelasticity effects. As a next step dissipative particle dynamics method is used for exploiting the behavior of surfactants under poiseuille flow. Morphology of micelles, velocity profile and density profile are examined and it will be shown that micelles migrate to the regions with maximum velocity and stretched in the flow direction. This behavior is shown in both reverse poiseuille flow and poiseuille flow with solid boundary. The steady velocity profiles are calculated. The results illustrate that, when surfactants are added to the water, the velocity profiles will be dampened and when driven force are raised, the average velocity will be increased.In high concentration of surfactant velocity profile will be flatted because of viscoelasticity effects. Key Words : Surfactant, Shear flow, Dissipative particle Dynamics Method, Viscosity, Viscoelastic fluid, Poiseuille flow.