We present a new approach to numerical modelling of incompressible flow of fluid about an elastically mounted rigid structure with large body motions. The solution is based on the Finite Volume Particle Method (FVPM), a meshless generalisation of the mesh-based finite volume method. The finite volume particles are allowed to overlap, without explicit connectivity, and can therefore move arbitrarily to follow the motion of a wall. Here, FVPM is employed with a pressure projection method for fully incompressible flow coupled with motion of a rigid body. The developed extension is validated for Vortex-Induced Vibration (VIV) of a circular cylinder in laminar crossflow. To minimise computational effort, non-uniform particle size and arbitrary Lagrangian-Eulerian particle motion schemes are employed, with radial basis functions used to define the particle motion near the cylinder. Close agreement is demonstrated between the FVPM results and a reference numerical solution. Results confirm the feasibility of FVPM as a new approach to the modelling of flow with strongly coupled rigid-body dynamics. (C) 2013 Elsevier Ltd. All rights reserved.