Abstract：A thorough study is carried out to answer whether the permeability coefficient of the fracture in rock is influenced by lateral stresses. The physical model and strict relative equations of rock mass with single fracture under 3D stresses are proposed by considering the tectonic characteristics of fracture in rock. In the model，it is supposed that the fracture in rock is composed of two body matrixes and the fracture is filled by soft material，whoes elastic modulus is much less than that of the body matrixes. Under 3D stresses，the coupling deformation of fillings and body matrixes makes the fillings dense and the permeability coefficient of the fracture decreased，in which the lateral deformation of the fracture plays significant role. The lateral deformation of body matrixes is equal to that of the fillings in fracture when the fracture is very narrow. Meanwhile the density of the fillings in the fracture will be changed with the lateral deformation and consequently the permeability coefficient of the fracture will be changed. The deduced calculation formula of permeability coefficient is examined by large amount of triaxial experimental data of coal and limestone. The simplified calculation formula of permeability coefficient with only normal stress is the same as traditional one. It is concluded that the lateral deformations caused by lateral stresses make important effects on the fracture seepage，whose relation is of the form of negative exponent law.
