In this paper, the particle method for handling oscillation of floating body using variable particle spacing is reported. Heave oscillation of floating mono hull and twin hull on the free surface in a viscous fluid is performed using Improved Meshless Local Petrov-Galerkin method based on Rankine Source function (IMLPG_R). The IMLPG_R method is a particle-based method that will solve the interaction between fluid and floating body using Navier-Stokes equation. The pressure at each time step is estimated from Pressure Poisson equation, in order to incorporate the heaving of the floating bodies, some improvements like free surface identification, gradient calculations has been introduced in the present paper to handle the variable resolutions in modelling. Simulations are performed for different frequency and amplitude of oscillations for mono and twin hull forced motions to show the robustness of the developed model to handle both small and steep oscillations. © 2019 Elsevier Ltd