Abstract Data for step—strain relaxation and cyclic compressive deformations of highly viscous short elastomer cylinders are modeled using a large strain rubber viscoelastic constitutive theory with a rate—independent friction stress term added. In the tests, both small and large amplitude cyclic compressive strains, in the range of 1% to 10%, were superimposed on steady state compressed strains, in the range of 5% to 20%, for frequencies of 1 and 10 Hz. The elastomer cylinders were conditioned prior to each test to soften them. The constants in the viscoelastic—friction constitutive theory are determined by employing a nonlinear least-squares method to fit the analytical stresses for a Maxwell model, which includes friction, to measured relaxation stresses obtained from a 20% step—strain compression test. The simulation of the relaxation data with the nonlinear model is successful at compressive strains of 5%, 10%, 15%, and 20%. Simulations of hysteresis stresses for enforced cyclic compressive strains of 20%±5% are made with the model calibrated by the relaxation data. The predicted hysteresis stresses are lower than the measured stresses.