We develop a non-associated flow rule (NAFR) based elasto-viscoplastic (EVP) model for isotropic clays. For the model formulation, we introduce the critical state soil mechanics theory (CSSMT), the bounding surface theory and Perzyna's overstress theory. The NAFR based EVP model comprises three surfaces: the potential surface, the reference surface and the loading surface. Additionally, in the model formulation, assuming the potential surface and the reference surface are identical, we obtain the associated flow rule-based EVP model. Both EVP models require seven parameters and five of them are identical to the Modified Cam Clay model. The other two parameters are the surface shape parameter and the secondary compression index. Moreover, we introduce the shape parameter in the model formulation to control the surface shape and to account for the overconsolidation state of clay. Additionally, we incorporate the secondary compression index to introduce the viscosity of clay. Also, we validate the EVP model performances for the Shanghai clay,the San Francisco Bay Mud (SFBM) clay and the Kaolin clay. Furthermore, we use the EVP models to predict the long-term field monitoring measurement of the Nerang Broadbeach roadway embankment in Australia. From the comparison of model predictions, we find that the non-associated flow rule EVP model captures well a wide range of experimental results and field monitoring embankment data. Furthermore, we also observe that the natural clay exhibits the flow rule effect more compared to the reconstituted clay.