In present research, the effect of surface suction on the stability of flow around an airfoil has been investigated. The overall purpose of this research is attaining laminar flow over the airfoil surfaces. Thus, the surface suction was applied to delay the flow transition point from laminar to turbulent and also to maximize the lift to drag ratio. For doing this, it is required to solve flowfield and to determine the transition point accurately. A CFD code in FORTRAN using an implicit Total Variation Diminishing (TVD) scheme was used to solve two-dimensional Navier-Stokes equations. For determination of transition point, the e N method was used. This method is based on the linear stability theory uses the eigenvalues of Orr-Sommerfeld equation for determining the amplification rates of disturbance waves. In the first part of thesis, the solution to Orr-Sommerfeld equation for the flow over a flat plate and the flow around NACA0012 airfoil was obtained. The results obtained are in good agreement with the results of other researchers. In this research, a finite difference method was used for solving the Orr-Sommerfeld equation. For validation of results obtained using the e N method, the results were compared with experimental data for the NACA0012 airfoil. In the second part of this thesis, flow control with surface suction around airfoil has been conducted. In order to validate the flow solver, the results of TVD code for flows with and without suction around the VFW-VF-2 airfoil compared with experimental data and a good agreement was observed. Next, an optimization process was performed to measure effects of parameters on surface suction such as the suction slot location and the extent of sucked flow through slots for the flow around NACA65 3 -018 airfoil. This process was aimed to control transition point using the results obtained from flow stability analysis. In all the cases studied, transition delayed using suction regardless of suction positions. However, the maximum delay in transition was obtained when the location of surface suction situated between the critical point and transition point. Because at this gap the flow disturbances are growing rapidly. For the aerodynamic coefficients in all suction cases, the lift coefficient was increased and the drag coefficient was decreased except a few cases. However, in all cases studied the lift to drag ratio was increased with surface suction. Another interesting feature of surface suction is removing or reducing the flow separation size which is observed in our results. Key Words: hydrodynamic stability analysis, boundary layer flows, Orr-Sommerfeld equation, transition prediction, e N method, laminar flow control, surface suction