Static and dynamic models of the characteristic responses of sliotar cores made of both cork and polyurethane were studied in this work in order to understand their constitutive behaviour. Data from quasi-static tests at 10 mm/s and from dynamic impacts at speeds from 5 to 25 m/s were used to develop and evaluate the models. The quasi-static response was described well by Hertzian theory. A non-linear HunteCrossley model and a modified linear KelvineVoigt model were used to predict the dynamic response with set mass and shape coefficient parameters. The HunteCrossley model predicted well both the maximum force and maximum deflection for each ball type. The HunteCrossley model generally captured the experimental contact times well with a mean difference between experimental and model contact times of 8.3%. The mean difference between the KelvineVoigt model and experimental contact times was 7.6%, while the corresponding mean difference for the coefficient of restitution was 13.1%. Overall, the modified KelvineVoigt model predicted the parameters of contact time and coefficient of restitution well. Contact time and coefficient of restitution prediction in this linear model were not particularly sensitive to the strain rate.