The Smoothed Particle Hydrodynamics (SPH) method has been widely used recently since its particle-based nature results in good characteristics for handling large topological deformation and small-scale features like bubbles, splashes and foams. In this thesis, the SPH method is exploited to animate various fluid behaviors. The first contribution of this thesis is proposing a method for viscoelastic fluids simulation. In order to achieve viscoelastic flow behaviors, an additional elastic stress term is included in the traditional Navier-Stokes (NS) equation. Also, each SPH particle is endowed with two attributes, viscosity and elastic stress coefficient. By updating the particle values of the two attributes according to the temperature variation, melting and flowing phenomena such as lava flow and wax melting can thereby be reproduced. We also propose a new method for high viscosity fluid simulation. A new elastic stress term, derived from a modified form of the Hooke’s law, is included in the NS equation to animate the movements of the high viscosity fluids. To eliminate the particle deficiency problem near the boundary, a corresponding ghost particle is created when the distance of a particle to the boundary is smaller than a certain threshold. We subsequently make an investigation on how the SPH method can be employed to conduct granular flow. The aforementioned elastic stress term for high viscosity fluid can also be used to handle the friction of granular materials. Additionally, viscosity force is added in the momentum equation to simulate dynamic friction which smoothens the velocity field and further maintains the simulation stability. Finally, we focus on the acceleration of fluid simulation. We extend the idea of adaptive sampling by defining two physical criteria on Reynolds number and vorticity, which are exploited to evaluate particle importance. When a particle’s corresponding values are smaller than the predefined Reynolds number and vorticity thresholds, it is labeled as unimportant. Then certain unnecessary calculations can be eliminated. Our experiments demonstrate that the method can be applied to improve the simulation performance without sacrificing visual quality