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, η∗12, depending both on strain rate, κ, and frequency, ω and were obtained for 10−2.5<κ<100.5 sec−1 and 10−2.5<ω<101.5 sec−1. The data were interpreted using the mechanical theory of materials with memory developed for both in‐line and orthogonal superposed flows. For a fixed κ, the η′12(κ,ω) data have a maximum value as ω→0, viz., η′12(κ,0), and with increasing ω, were found to approach the no‐shear data, η′(ω). Also, the theoretical prediction, η′12(κ,0) = [dκη(κ)/dκ], was experimentally confirmed over the entire range of κ measured. For small ω, G′12 = γ12(κ)ω2 with γ12(κ)>0, and γ12(κ)→−γ (the second‐order fluid normal stress coefficient) as κ→0. Further, the relation, (G′12/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)/η′12(κ,0)], was used to correlate nondimensionalized forms of the η′12 and G′12 data. Also, the particular strain‐rate‐dependent stress‐relaxation functions ψ12(κ,σ), used to define η∗12(κ,ω), were calculated and indicate a decrease in material memory with shear.