During the last three to four decades, the field of particle motion in visco-elastic liquids has witnessed years of unprecedented growth and consequently, significant advances have been made to our understanding of the underlying fluid dynamical phenomena. Such studies have been motivated by two distinct but interrelated perspectives. First, an adequate knowledge of gross fluid mechanical aspects such as the drag force acting on a particle moving in a visco-elastic medium is frequently needed in a range of process engineering applications including sedimentation of muds and suspensions, handling of fluid systems, falling ball viscometry, microrheometry in diffusing wave spectroscopy (Levine and Lubensky, 2001), formation of weldlines in polymer processing (NguyenChung et al., 1998), in assembly process for anisotropic conductive joints (Ogunjimi et al., 1995), and in biological processes (Holzwarth et al., 2002; Foo et al., 2004) etc. Second, the flow over a sphere or a cylinder yields a complex (but free from geometric singularities) nonviscometric flow and it thus affords a fairly stringent test for establishing the validity of visco-elastic fluid models whose parameters are invariably evaluated from data obtained in well-defined flows. These two objectives coupled with the simplicity of the geometry have also made such flows very attractive for the validation of numerical solution procedures. In view of all these features, the creeping motion of a sphere in a visco-elastic fluid filled in a cylindrical tube (sphere-to-tube diameter ratio of 0.5) and the uniform flow over a long cylinder in a planar slit (cylinder diameterto-slit width ratio of 0.5) have been used extensively for the benchmarking of a diverse variety of numerical solution procedures developed and adapted for computing visco-elastic flows (Brown et al., 1993; Szady et al., 1995; Saramito, 1995; Owens and Phillips, 2002). Concentrated efforts have led to the development of highly refined and very successful numerical algorithms for computing steady and unsteady visco-elastic flows (Keunings, 2000; Reddy and Gartling, 2001; McKinley, 2002; Owens and Phillips, 2002; Petera, 2002). The exponential growth in the numerical activity in this field has also been matched by the development of elegant and improved experimental techniques for resolving the spatial and temporal features of the flow field around submerged objects.