Elasticities were measured under the conditions of shear and elongational flows of PEO and Separan solutions below the concentration level of several tens of ppm. The first normal stress difference in a shear flow was measured by utilizing reactions exerted by a jet issuing from a capillary, and the elongational stresses were also obtained separately with reactions or pressure drops produced in the flow through small orifices. The following points were clarified: the first normal stress difference τ₁₁-τ₂₂ had a relationship of the power law type with the shear rate γ, that is, τ₁₁-τ₂₂&prop;γ. For the PEO 5 ppm solution, the power law index s was 2.0, as predicted with the Maxwell model, and in this case, the relaxation time was determined as 0.0016 second. For the other solutions used, we had 1.2< s < 2.0 and the measured first normal stress differences could be expressed with a modified Maxwell model. The elongational stresses measured with the two methods of jet reaction and pressure drop generally agree with each other. The elongational stress can be expressed, albeit approximately, with the Maxwell model or the modified Maxwell model depending on the concentration of the solution used. In some cases, the elongational stresses of PEO solutions, at least qualitatively, agree with predicted values of the yo-yo model proposed by Ryskin.