Flow of dilute polymer solutions is known to exhibit purely elastic instabilities even in the case of negligible fluid inertia. Such instabilities are observed and studied in flow with curvilinear streamlines, and are attributed to the generation of elastic stresses due to the stretching of polymers in the flow.  We show a new elastic instability that is identified between two cylindrical obstacles, which are embedded in the linear channel flow and are far away from the channel walls.  The instability appears as vortices (counter flow) which initiates in the vicinity of the second obstacle above the critical value of Weissenberg number (Wi) and spans the region between the obstacles with increasing Wi. The transition to the observed flow instability is characterized by the estimated friction factor through measured pressure drop and fluid discharge rate, and by vorticity, i.e., curl of flow velocity, obtained from particle image velocimetry.