An instrument is described which was designed to measure the elastic and viscous properties of liquids, primarily of solutions of linear high polymers whose elastic properties had already been observed qualitatively The liquid is contained in a narrow annulus between two long vertical cylinders. The outer cylinder can be driven in steady rotation at a known speed, or in harmonic angular oscillations of known amplitude and frequency. In steady rotation, the torque on the stationary inner cylinder is measured at different speeds, and interpreted to give a viscosity coefficient as a function of shear stress. In oscillatory motion, the amplitude of oscillation of the inner cylinder, when constrained by a torsion wire, is measured and plotted against the frequency The shape of the resulting graph can be interpreted so as to distinguish and measure different types of elastic behaviour. The annular gap, the restoring constant of the torsion wire and the amplitude of oscillation of the outer cylinder can be varied in discrete steps. The angular velocity of the outer cylinder can be varied continuously from 0 3 to 3,000 rev/min in steady rotation, and the frequency can be varied continuously from 0.25 to 25 c/s. in steady oscillation The performance of the instrument in both steady-state and oscillatory experiments is assessed by comparing observed and predicted results for Newtonian liquids of known viscosity. An example is given of the behaviour of a typical polymer solution in both kinds of experiment, together with a suggested quantitative interpretation of the results.