This article presents a permanent magnet planar translational generator which is able to exploit multiple modes of sea wave energy extraction. Linear electrical generators have recently been studied for the exploitation of sea wave energy, but, to the best of our knowledge, no synchronous planar translational generator has been proposed. In this article, to maximize the energy extraction, we have considered all the potential modes of motion due to wave excitation and included them within the mathematical model of the proposed system. The principle of operation of the generator can be summarized as follows: the moving part (translator) of the generator is driven from the sea waves and induces and electromotive force (EMF) on the windings mounted to the armature. The movement of the translator is 2-D and, therefore, all the movement modes of the wave, except heave, can be exploited. The proposed mathematical model includes the dynamic equations of the translator and the electric equations of the windings. The coupling parameters (inductances and fluxes) have been determined by finite element method analysis. Optimization of the device has been performed by considering both, the parameters of the electromagnetic circuit, and, the parameters associated with the stochastic features of the wave.