This research study was devoted to the modeling of the mechanical behavior of three carbon black/silica natural rubber/butadiene rubber (NR/BR) compounds under a tensile load. These compounds were prepared on a two-roll mill, and the tensile testes were carried out on a dumbbell-shaped specimen and three rubber-strip specimens with different widths. Heat buildup tests were also performed, and the temperature rise was determined. The time-independent behavior of the rubber was described by traditional hyperelastic models, including those of Marlow and Yeoh. The viscoelastic behavior was studied with two linear (Prony series) and nonlinear [BergstromBoyce (BB)] models. A previously developed methodology by the authors, which was based on the finite element modeling of the tension of the rubber strips, was used to determine the parameters of the mentioned equations. It was shown that neglecting the viscoelasticity would have given rise to large errors in predicting the mechanical deformation in the rubbers. However, the linear viscoelastic model failed to predict the correct behavior at a large strain, particularly for wider samples. On the other hand, not only could the combination of the Yeoh hyperelastic model with the BB equation describe the mechanical behavior at low to medium strains, but also the large strains were taken into consideration. Both the linear and nonlinear hyperviscoelastic models accurately described the hysteresis in rubbers, and this could be used for the evaluation of the rolling resistance in tires. (c) 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013