An approximate theoretical treatment is presented for the large deformation of non-linear viscoelastic cylindrical blocks bonded between rigid end-plates. The measured compressive force relaxation of two blocks of different initial radius to height ratios is shown to be in good agreement with the theoretical predictions for a carbon-black filled vulcanizate. Measurements of dynamic stiffness k* (=k1+jk2) for various compressive pre-loads and a frequency range of .05 to 30 Hz were also conducted. The measured values for the storage stiffness, k1 are shown to be in good agreement with the theoretical predictions, but poor correlation between experiment and theory is obtained for the loss stiffness, k2. Discrepancies between experimental and analytical results are attributed to the approximations employed to make the analysis mathematics more tractable rather than to the basic theory involved. Such approximations were necessary in lieu of the lack of commercially available finite difference or finite element computer codes for treating the subject problem in a more exact manner.