In this paper, the periodic viscoelastic shedding flow of Giesekus fluid past an unconfined square cylinder is investigated numerically for the first time. The global quantities such as lift coefficient, Strouhal number and the detailed kinetic and kinematic variables like normal stress differences and streamlines have been obtained in order to investigate the flow pattern of viscoelastic flow. The effects of Reynolds number and polymer concentrations have been clarified in the periodic viscoelastic flow regime. Our particular interest is the effect of mobility parameter on the stability of two dimensional viscoelastic flows past an unconfined square cylinder. To fulfill this aim, the mobility parameter has been increased from 0 to 0.5 for different polymer concentrations. Results reveal that mobility factor noticeably affects the amplitude of lift coefficient and shedding frequency more strongly at higher polymer concentrations.

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