The numerical simulation of time-dependent two-dimensional inertial viscoelastic flows around a circular cylinder is investigated. The simulation is performed by employing a second order parallelized finite volume method (FVM) in both spatial and the temporal domain. Giesekus model is used as a non-linear rheological constitutive equation. The numerical results of inertial viscoelastic flow behind a circular cylinder illustrate the significant effect of the fluid elasticity on the flow structure. The impact of the elasticity on the recirculation region and shedding frequency are discussed. Also, the effects of mobility factor on the shedding frequency of two-dimensional viscoelastic flows past a confined cylinder are studied. The results reveal that enhancing the mobility factor causes a noticeable increase in the vortex shedding frequency and flow instability. (C) 2013 Elsevier B.V. All rights reserved.