Abstract: The mechanical performance of granular materials has much randomness, The influence of randomness on the constitutive relations for granular materials is studied. Based on incremental endochronic constitutive relations for granular materials, the relationship between the statistic eigenvalue of stress increment and that of material parameters is investigated by considering the randomness of material parameters and using the small parameter perturbation law. The influence of randomness of each parameter on the stress is discussed. The perturbation expression of incremental endochronic constitutive relations for granular materials is established and the parameters in the perturbation expression are determined. The mean value and variance of the stress increment are obtained from those of material parameters. An example is studied to verify the practicability of the method.