Abstract:A new heterogeneous constitutive model of random porous rock is established by introducing two model parameters:the local radius(r) and the local porous density(p). In this model,the local radius(r) and the local porous density(p) are used to describe the length of the porous medium and the local porous space density in each distributed porous zone respectively. The elastic properties of rocks containing a random spatial distribution of porous size can be simulated by this model with the connection of the macro-mechanical properties(the elastic wave speeds) of the porous rocks and the model parameters(r and p). Numerical example indicates that the real heterogeneous medium can be modeled effectively as long as appropriate model parameters are given. Different heterogeneous random porous rocks have different scattering effects on wave speeds. The elastic wave speeds caused by larger pore are more distinguishable. The relative random distribution characteristics of pores hardly affect wave speeds under the same random distribution of the local porous density and local radius. The resolving power of S-wave on random porous rock is stronger than that of P-wave,and S-wave is more sensitive to anisotropy caused by micro-cracks.