The adaptations of the SPH method for simulating incompressible fluids which focuse on two features: the surface tension and artificial viscosity, are presented in this article. The background and principles of the SPH method are explained and its application to incompressible fluids simulations is discussed. The methodology and implementation of artificial viscosity in the SPH method are presented. The modification for surface tension simulation, which relies on incorporating additional forces into the model, as well as the methodology are suggested. Also, the new equations for artificial viscosity are presented, which are able to simulate a flow of non-newtonian fluids. The results obtained with the method are presented and discussed.