A new computational program, which is based on the CIP/CCUP(Constraint Interpolation Profile/CIP Combined Unified Procedure) method, has been developed to numerically analyse sloshing phenomena dealt as multiphase-flow problems. For the convection terms of Navier-Stokes equations, the RCIP(Rational function CIP) method was adopted and the THINC-WLIC(Tangent of Hyperbola for Interface Capturing-Weighted Line Interface Calculation) method was used to capture the air/water interface. To validate the present numerical method, two-dimensional dam-breaking and sloshing problems in a rectangular tank were solved by the developed method in a stationary Cartesian grid system. In the case of sloshing problems, simulations by using a improved MPS(Moving Particle Simulation) method, which is named as PNU-MPS(Pusan National University-MPS), were also carried out. The computational results are compared with those of experiments and most of the comparisons are reasonably good.