This paper incorperates Bingham and bi-viscosity rheology models with the Navier-Stokes solver to simulate the dynamics and kinematics processes of slumps for tsunami generation. The rheology models are integrated into a computational fluid dynamics code, Splash3D, to solve the incompressible Navier-Stokes equations with volume of fluid surface tracking algorithm. The change between un-yield and yield phases of the slide material is controlled by the yield stress and yield strain rate in Bingham and bi-viscosity models, respectively. The integrated model is carefully validated by the theoretical results and laboratory data with good agreements. This validated model is then used to simulate the benchmark problem of the failure of the gypsum tailings dam in East Texas in 1966. The accuracy of predicted flood distances simulated by both models is about 73% of the observation data. To improve the prediction, a fixed large viscosity is introduced to describe the un-yield behavior of tailings material. The yield strain rate is obtained by comparing the simulated inundation boundary to the field data. This modified bi-viscosity model improves not only the accuracy of the spreading distance to about 97% but also the accuracy of the spreading width. The un-yield region in the modified bi-viscosity model is sturdier than that described in the Bingham model. However, once the tailing material yields, the material returns to the Bingham property. This model can be used to simulate landslide tsunamis.