The paper investigates the viscoelastic behaviour of blood over low value of elasticity, to analyse the influence of inertia in the presence of elasticity. For viscoelastic fluids shear-thinning and strainsoftening PTT (Phan-Thien/Tanner) constitutive model is employed to identify the influence of elasticity. The computational method adopted is based on a finite element semi-implicit time stepping Taylor- Galerkin/pressure-correction scheme. Simulations are conducted via atherosclerotic vessels along with various percentages of deposition at distinct values of Reynolds numbers. The numerical simulations are performed for recirculation flow structure and development of recirculation length to investigate the impact of atherosclerosis on partially blocked plaque deposited vessels.