Abstract: Because of the sedimentation of soil, many foundationscan be considered as transversely isotropic. In this article, based ontheories of mathematics and mechanics, the constitutive model of atransversely isotropic foundation is proposed together with the methods ofdetermining related parameters.The model is found easy to use in engineering. As far as the sedimentation of soilis concerned, the constitutive model gives more realistic stress and strain response than the isotropic model.