A computerized apparatus for the measurement of low shear rate viscosity on polymer solutions at elevated pressure and temperature is described. The pressure is variable from 1 bar to 400 bar with an accuracy of +/- 5 bar. The temperature is variable from 0 degrees to 100 degrees C with an accuracy of +/- 0.3 K. The instrument is operated in a free-relaxation mode in which the decay of oscillation of the torsion pendulum after an initial displacement is recorded and used to compute the viscosity of the sample. The measurements are performed according to the contents of a user-specified control file, and the oscillation data are stored digitally and later analyzed for parameter estimation. The instrument operates in the very-low frequency range (0.03 to 0.25 Hz) and the accuracy of the measured viscosity is +/- 0.03 x 10(-3) Ns/m(2).