Smoothed Particle Hydrodynamics (SPH) is a mesh-free lagrangian method. It is a particle base method in macroscopic scale, works by dividing the fluid into a set of discrete elements, referred to as particles rather than mesh cell. These particles have a spatial distance (known as the "smoothing length"), over which their properties are "smoothed" by a kernel function . This means that the physical quantity of any particle can be obtained by summing the relevant properties of all the particles which lie within the range of the kernel. Every particle carries mass, velocity, pressure and different hydrodynamic variable. SPH First applied to astrophysics and proves to be well suited for studying complex fluid dynamics. This method has been successfully used to model free-surface flows especially when strong free-surface deformations take place. The simulation of the incompressible flow is normally carried out by two methods in SPH: first, approximately simulating incompressible flow with a small compressibility, called Weakly Compressible SPH (WCSPH); second, fully incompressible procedure that called Incompressible SPH (ISPH). In the first method pressure has been obtained from a state equation and in the next one, from a poisson equation. In the WCSPH to satisfy Courant-Friedrichs-Lewy (CFL) condition, the time step is limited to very small value by the speed of sound. Also compressibility cause sound wave reflection at the boundaries which can lead to numerical instability. In the ISPH the CFL condition is based on the fluid velocity field rather than the speed of sound and therefore large time step can be used in the simulation. In this thesis, attention is focused on the boundary condition specially In-flow/ Out-flow boundary condition. In Eulerian models the imposition of inflow and outflow boundary conditions is relatively simple because each cell of the mesh describes a part of the domain and ghost cells can be used to impose boundary conditions. Conversely, the implementation of suitable inflow/ outflow boundary condition in the SPH model is not straightforward because of the Lagrangian nature of this scheme. Indeed SPH particle move during the simulation and, consequently, they have to be conveniently inserted and removed from the domain. Furthermore, the interpolation procedure which is the basis of the SPH scheme makes the implementation of this kind of boundary condition difficult. Moreover, the fractional step algorithm, which compute intermediate velocity, pressure and location for particles, increase complexities. In this thesis, we present a new idea to overcome most of these difficulties. In this method, some particle are defined at solution domain at each time step. At the solid boundary these particles are fixed and never need to be detected in each time step. But at the inlet/ outlet boundary, particles are moving; so we need to mark them in every time step. By constructing a simple grid, this aim is obtainable. These boundary particles can be used for implementation of boundary condition. First the proposed idea is used for 2D internal flow in channel flow. The suitability of the in/ out-flow model is shown by comparing the obtained velocity field with the analytical solution. Then capabilities of the algorithm are tested in Backward-facing step flow which is a more complicate flow that need in/ out-flow boundary conditions. The result are validated with standard solution obtained from a Finite Volume Method (FVM) in different Reynolds number. At the end the flow in an open-cavity is simulated. Key words SPH, ISPH, Incompressible flow, Projection method, In/Out-flow boundary condition