Abstarct: The study of flow around a circular cylinder is an interesting and practical topic in fluid dynamics that nominated as a benchmark problem of the computational flow communities. This problem has no singularity, either in the geometry or in the boundary condition. Also, cylinder flow is rich in physical effects such as shear laxyers, recirculation regions, boundary laxyer and vortex dynamics. The present work represents the numerical investigation for time-dependent inertial viscoelastic flows around a bluff body. The simulation is performed by a parallelized finite volume method (FVM) using second order in both the spatial and the temporal discretization. Here, The Giesekus rheological model is used as a constitutive equation of viscoelastic flow. Since the viscoelastic functions of the Giesekus rheological model are perfect and is found to have the ability for describing the normal stress differences, it is used as a constitutive equation. The results for the viscoelastic flow are compared with those for a Newtonian flow. Frequency of the vortex shedding is shown to be attenuated by elasticity of the fluid, while the recirculation region behind the cylinder is elongated before reaching the critical Reynolds number. These results are in agreement with recent experimental and numerical observations. Our particular interest is the effect of mobility parameter on the stability of two dimension viscoelastic flows past a confined cylinder. In particular, our results reveal that the greater the maximum mobility parameters, the larger the value of the vortex shedding frequency. Thus, the stabilization brought to bear by the presence of the Giesekus would appear to depend strongly upon the mobility parameters of the polymer solution.