A comprehensive study of the rheological characterization of the aqueous solutions of PEO (Polyethylene Oxide) with molecular mass of 4×10⁶, 5×10⁶ and 8×10⁶ g/mol respectively named (4miDA), (5miDA) and (8miDA) was conducted. A large batch of samples of 4miDA PEO with concentrations varying from 0.1% to 3% representing the range of dilute solutions to very high viscous hydrated gels, were tested. Steady state shear flow and oscillatory measurements are reported. Cross, Carreau and Carreau-Yasuda models were used to describe the shear-thinning behaviour within the shear rate range (0.001 ≤ $γ•$ ≤ 3000 s^-1). Experimental findings were validated with published results under the same operating conditions within specified shear rate ranges (0.1≤ $γ•$ ≤100 s^-1). We find that the behaviour of PEO under shear is highly dependent on the rheometer, material and operating procedures. Oscillatory measurements were carried out to determine the complex properties of the PEO solutions in the frequency ω and strain amplitude γ ranges of (0.01 ≤ ω ≤100 rad/s) and (0.01 ≤ γ ≤1000 %), respectively. Higher magnitudes of dynamic moduli (G^/ & G^//), zero (η₀) and infinite (η_∞) shear rate viscosities, resonant frequencies (ω_res), linear viscoelastic regions (LVER), and higher relaxation time constants (λ) were observed with increasing concentration and molecular weight. The rheological response of the PEO polymeric solutions was further clarified via Lissajous curves. The aim of this work is to characterize the behaviour of the 4miDa PEO prior to its use in an experimental investigation of the secondary flows of viscoelastic fluids in non-circular channels.