Particle image velocimetry (PIV) is used to measure the full-field instantaneous velocity in the inertialess, viscoelastic flow past a confined circular cylinder. Instantaneous fields of velocity vectors are obtained over an entire plane for the creeping motion of a highly viscoelastic fluid. In all cases considered, a fixed aspect ratio (channel half width to cylinder radius) of 16 was used. Our results indicated that at relatively low Deborah number (De), i.e. low flow rates, of 0.6 and 1.2, the flow reached steady-state conditions rapidly (i.e. less than or equal to 10 s). But as the flow rate is increased (or De is increased), e.g. De = 1.8 and De = 2.4, the viscoelastic flow may require as long as 90 s to reach steady flow. We also conducted experiments for steady, viscoelastic flow past an off-centered cylinder in the channel. Instantaneous full-held velocity and vorticity fields are examined for flow past an eccentrically-placed cylinder between parallel channels for various values of the eccentricity parameter (epsilon). Measurements are made at different values of Deborah number. It is seen from these studies that the spatial structure of the flow field, the vorticity intensity, and the spatial characteristics of vorticity field are all strongly affected by rheological parameter (elasticity) and geometric parameter (eccentricity).