We present a two-dimensional computational flow solver for simulation of two-way interactions between moving rigid bodies and two-fluid flows. The fluids are assumed to be incompressible and immiscible. The two-step projection method along with Graphics Processing Unit (GPU) acceleration is employed to solve the flow equations. The fluid-solid interaction is captured by using the fictitious domain method. A consistent mass and momentum scheme is implemented, which allows for simulation of multiphase flows characterized by large density ratios. The evolution of interfaces in the three-phase system is tracked by using the volume-of-fluid method with two scalar functions, representing the solid domain and one of the fluids. A geometrical approach is employed to reconstruct the interfaces in cells containing three phases and capture the intersection of phase interfaces (triple point). The performance and accuracy of the flow solver are assessed through a set of canonical test cases. Then, it is used to simulate the interactions between a free-floating buoy and waves generated by a bottom-hinged paddle in a wave tank. © 2014 Elsevier Ltd.