The response of concentrated solutions (0.7 g/dl‐2.0 g/dl) of poly(ethylene oxide) (Polyox WSR‐301) to in‐line shearing oscillations was measured using a Weissenberg Rheogoniometer Model R.18 with the parallel‐plate geometry. This physical system was analyzed using the theory of Pipkin and Owen (Phys. Fluids,10, 836, 1967) for nearly viscometric flows and explicit formulae for rheological parameters in terms of measured quantities were obtained in the limit of negligible fluid density. The data are presented as the complex viscosity,η12*,depending both on strain rate, κ, and frequency, ω and were obtained for10−2.5<κ<100.5 sec−1and10−2.5<ω0,andγ12(κ)→−γ(the second‐order fluid normal stress coefficient) asκ→0.Further, the relation,(G12′/ω2)=(σ2−σ1)/(2κ2),was found to be valid to a higher order in κ than predicted by the theory. A material time,τ(κ)=[γ12(κ)/η12′(κ,0)],was used to correlate nondimensionalized forms of theη12′andG12′data. Also, the particular strain‐rate‐dependent stress‐relaxation functionsψ12(κ,σ),used to defineη12*(κ,ω),were calculated and indicate a decrease in material memory with shear.