In this study we consider PCF (Plane Couette Flow) which is introduced by two parallel planes which have same velocity in opposite direction and the distance between them is filled by viscoelastic fluid. By this way we have modeled viscoelastic damper. The constitutive equation of JS (Johnson-Segalman) has been used for dynamic analysis of viscoelastic damper’s behavior. By using this equation we can examine normal stress which is existed in the fluid and achieve more accurate results about stability of flow between two planes. At first problem formulation is covered. The general conservation and constitutive equations, as well as the boundary and initial conditions are covered for a JS fluid. The Galerkin projection is applied, using Chandrasekhar functions, for 1-D disturbance from the base (Couette) flow. An arbitrary number of modes are included, to lowest order, the formulation leads to a six-dimensional system. Linear stability analysis around the base flow and nontrivial steady-state solution branches is carried out. The influence of inertia on transient flow is studied. Discussion and concluding remarks are finally given. This study has been done specially for PCF of fluids with high molecular weight such as combination of a Newtonian solvent and a polymer solute.