The present study investigates the vortical and nonlinear effects in the roll motion of a 2-D body with square cross-sections by using Smoothed Particle Hydrodynamics (SPH). A 2-D rigid body with square cross-section is taken into account for the benchmark study and subjected to the oscillatory roll motion with a given angular frequency. The governing equations are continuity equation and Euler's equation with artificial viscosity term. Weakly Compressible SPH (WCSPH) scheme is employed for the discretization of the governing equations. Velocities of the fluid particles are updated by means of XSPH + Artificial Particle Displacement (VXSPH+APD) algorithm. In this method only the free surface fluid particles are subjected to VXSPH algorithm while the APD algorithm is employed for the fully populated flow regions. The hybrid usage of numerical treatment keeps free surface particles together by creating an artificial surface tension on the free surface. VXSPH+APD is a proven numerical treatment to provide the most accurate results for this type of free surface flows (Ozbulut et al. 2014). The results of the present study are compared with those of the experimental studies as well as with those of the numerical methods obtained from the current literature.