The goal of this work is to study the dynamics of floating platforms that are designed for marine energy generation. This work is done in collaboration with Tecnalia R&I, a company settled in the Basque Country which designs this kind of platforms. To our purpose we present a method for the simulation of two-phase flow with the presence of floating bodies. We consider the variable density incompressible Navier-Stokes equations and discretize them by the finite element method with a variational multiscale stabilization. A level-set type method is adopted to model the interphase between the two fluids. The mixing or smearing in the interphase is prevented with a compression technique. Turbulence is implicitly modeled by the numerical stabilization. The floating device simulation is done by a rigid body motion scheme where a deforming mesh approach is used. The mesh deforms elastically following the movement of the body. Simulation of a decay test on a cube is performed and the results are presented in this paper. All the simulations are done with the open source finite elements parallel software FEniCS-HPC.