Utilizing the experimental and modeling approaches, the Gamma radiation effects on stress responses of the silicon rubber foam under quasistatic compression are investigated. In the experimental work, the samples of the silicon rubber and the silicon rubber foams are quasistatically compressed before and after the Gamma radiation (a dose of 500 kGy and a dose rate of 100 Gy/min). The data reveal that the Gamma radiation obviously increases the material hardness, e.g., the compressive stresses of the silicon rubber and the silicon rubber foams both increase over 5 times as the strain is 20%. In the simulation work, a multiscale method combined with finite element method is developed to numerically predict the compressive stress of the silicon rubber foams. The microscale models are first constructed based on the real microstructures of the silicon rubber foams. The compressive stress and strain relation before and after the Gamma radiation is then simulated and obtained utilizing the phenomenological constitutive models based on the testing data of the silicon rubber. The simulation reveals that the Gamma radiation strongly affects the compressive response of the microscale models. The stress responses of the microscale models are then transferred into the macroscale models. The results also prove that the Gamma radiation obviously increases the hardness of the macroscale models. Data comparison shows that the numerical results agree with the testing data well, which verifies the developed method. The present work develops a new method to predict the radiation effects on mechanical properties of rubber foams.