Abstract: The bedded carbonaceous slate exhibits transversely isotropic creep properties. The creep behaviors of carbonaceous slate are studied using the triaxial compressive creep tests on horizontal bedding specimens and vertical bedding specimens. The creep flow direction is analyzed with the experimental data. It is found that the creep flow directions of the horizontal and vertical bedding specimens are different. A creep constitutive model for transversely isotropic rocks is proposed. The constitutive model is composed of creep potential function based on the generalized octahedral shear stress and creep non-associated flow law. The creep equation is formulated as a function of stress and the irreversible strain, which is defined as an internal state variable. The method for determining the model parameters is proposed. The creep model, along with the method of parameter determination, is validated using the test data from this study and literatures. The effect of strain rate on initial creep state is discussed using the model. The results provide a theoretical basis for understanding the transversely isotropic creep behaviors of rocks and enriching the basic theory of rock mechanics.