Abstract: The definition of a plastic time is presented and the intrinsic time suggested by Valanis K C is that of a specific case. Through analyzing the fundamental behavior of ‘present approximate equation’ of an integral endochronic model in terms of plastic time, the author reveals the necessary condition that yield surface and plastic potential exist in the ‘present approximate equation’. If the ‘present approximate equation’ has yield surface and plastic potential, the plastic factor of the ‘present approximate equation’ is equal to the product of the plastic time and Pfaffy’s integral denominator. When Pfaffy’s integral denominator is a positive constant, the plastic factor is equal to the plastic time. The endochronic model of dry sand with small strain is derived from the classical increment plastic theory in which the plastic time is used as the plastic factor. This model can well describe the dilatancy of sand and simulate the stress-strain response of dry sand due to cyclic loadings.