Smoothed Particle Hydrodynamics (SPH) arises as a useful tool in analyzing violent fluid flow problems with a free surface. The present study treats 2D nonlinear fluid motions with a free surface by means of SPH method. As a Lagrangian based method, SPH is employed first for the solution of the 2-D dam break problem, which can be used as a benchmark study, using Euler's equation and continuity equation as the governing differential equations. While the usual mathematical treatments of SPH are adopted, the assumptions or empirical schemes and parameters used by previous researchers are revisited to see the effect of these parameters-such as epsilon in "XSPH" variant velocity-on the resultant fluid flow. It is observed that such parameters, which find widespread acceptance, have crucial effects on the evolution of the flow. 2D sloshing problem of a swaying partially filled rectangular tank is subsequently investigated. It is understood from the numerical investigations that it is possible to obtain acceptable, valid results by tuning the basic parameters (such as epsilon in "XSPH") without further developing new techniques such as density re-initialization and particle refinement to improve flow characteristics.