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A flowing soap film is a promising test bed to generate two-dimensional turbulence dominated by an extensional stress field. In this study, the effects of visco-elastic fluid on two-dimensional (2D) turbulent flow have been quantified by the curvature of vortices visualized by a Film Interface Flow Imaging (FIFI) method in the flow. The curvatures of the vortices are related to the direction of velocity vector on the vortices. In order to confirm this idea, the velocity field of 2D turbulent flow was obtained by Particle Image Velocimetry (PIV). As a flexible polymer, polyethyleneoxide (PEO) was also added to the flow in order to observe how polymers vary the curvature histogram and velocity fields. From the results, it was found that the variance of the curvature histogram became lower by adding the polymer. This was also confirmed by the phenomena that the fluctuation of the velocity vectors in the normal direction becomes small by adding the polymer.