Background Understanding the mechanical response of elastomers to applied deformation at different strain rates and temperatures is crucial in industrial design and manufacture; however, this response is often difficult to measure, especially at high strain rates (e.g. > 100 s(- 1)), and more predictive methods to obtain constitutive relationships are required. Objective The objective of the research described in this paper is to develop such methods. Method The paper outlines a novel approach combining quasi-static monotonic tests in tension and compression, quasi-static cyclic tests in tension, and high strain rate tests in compression, with dynamic mechanical analysis and time-temperature superposition. A generalized viscoelastic model incorporating continuum damage is calibrated. Results The results show that a model calibrated using data from quasi-static compression and dynamic mechanical analysis can be used to adequately predict the compressive high strain rate response: hence, this paper provides an important step in the development of a methodology that avoids the requirement to obtain constitutive data from high strain rate experiments. In addition, data from FE models of the dynamic mechanical analysis experiments are provided, along with a discussion of data obtained from tensile and cyclic loading. Conclusions The paper demonstrates the effectiveness of 'indirect' predictive methods to obtain information about high rate behaviour of low modulus materials.