A floating body with substantial heave motion is a challenging fluid–structure interaction problem for numerical simulation. In this paper we develop SPH in three dimensions to include variable particle mass distribution using an arbitrary Lagrange–Eulerian formulation with an embedded Riemann solver. A wedge or cone in initially still water is forced to move with a displacement equal to the surface elevation of a focused wave group. A two-dimensional wedge case is used to evaluate two forms of repulsive-force boundary condition on the body; the force depending on the normal distance from the object surface produced closer agreement with the experiment. For a three-dimensional heaving cone the comparison between SPH and experiment shows excellent agreement for the force and free surface for motion with low peak spectral frequencies while for a higher peak frequency the agreement is reasonable in terms of phase and magnitude, but a small discrepancy appears at the troughs in the motion. Capturing the entire three-dimensional flow field using an initially uniform particle distribution with sufficiently fine resolution requires an extremely large number of particles and consequently large computing resource. To mitigate this issue, we employ a variable mass distribution with fine resolution around the body. Using a refined mass distribution in a preselected area avoids the need for a dynamic particle refinement scheme and leads to a computational speedup of more than 600% or much improved results for a given number of particles. SPH with variable mass distribution is then applied to a single heaving-float wave energy converter, the ‘Manchester Bobber’, in extreme waves and compared with experiments in a wave tank. The SPH simulations are presented for two cases: a single degree-of-freedom system with motion restricted to the vertical direction and with general motion allowing six degrees-of-freedom. The motion predicted for the float with general motion is in much closer agreement with experimental data than the vertically constrained system. Using variable particle mass distribution is shown to produce close agreement with a computation time 20% of that required with a uniformly fine resolution. Copyright © 2012 John Wiley & Sons, Ltd.