A concentrated polymer solution is sheared by a rod oscillating axially with a very small amplitude in a closed tube. The rod is driven by a coil in a magnetic field; from electrical measurements on the coil, the mechanical resistance and reactance of the system are calculated by transducer relationships. Equations are given for obtaining the dynamic viscosity, &eegr;′, and rigidity,G′, of the solution. In the case of some polymer solutions, the audiofrequency range covered by the present apparatus falls in the dispersion zone where &eegr;′ andG′change rapidly with frequency. In other cases the frequency range covered appears to be at the upper end of the dispersion zone; &eegr;′ is far smaller than the viscosity in steady flow, andG′changes very little with frequency. The advantages and limitations of the method are discussed.