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Anisotropy analysis is important to understand reservoir properties, especially for shale formation. In this paper, the velocity and permeability anisotropy of Barnett Shale were measured at laboratory condition. A new method was developed to determine the elastic constant C₁₃ in order to reduce uncertainty caused by the cutting angle error at 45 degree to bedding planes. The effects of the Young’s modulus and Poisson’s ratio in terms of Thomsen’s anisotropy parameters were discussed. Our goal is to understand the relationship between wave propagation and fluid flow in the medium with vertical transverse isotropy (VTI) type of symmetry. Strong correlation between elastic constant C₄₄ and permeability parallel to the bedding planes has been identified.