Abstract：We introduce the macroscopic model of nonlinear elastic materials，Preisach-Mayergoyz model(PM model). PM model is founded by the response of the pair of stresses( )of many hysteretic mesoscopical units(HMU)versus loading and unloading；and it¢s nonreversible through the original path. Porous saturated rocks have characters of hysteresis and discrete memory to describe. Based upon the hypothesis that the macro nonlinear elastic properties of porous rock are caused by an enormous variety of mesoscopical structural features such as cracks，joints and contacts；we have simulated hysteresis and discrete memory in rock by the PM model. The curves of stress-axial strain，stress-radial strain in the rock are determined by the space density and elastic properties of HMU in PM model. The elastic moduli have close relation with distribution of PM space density and a pair of equilibrium length of HMU. The treatment in PM model emphasizes the importance of stress history in the determination of the elastic state of a rock. The PM space density reflects the constitutive relationship response of a rock under cyclic loading in some degree. We argue that hysteresis is the cause of discrete memory in rock through the simulation of a rock¢s discrete memory. We can also use the equation of the stress-strain state to simulate the discrete memory of a rock observing in the experiment.
