The invention relates to a wave power assembly having a hull and a linear electric generator. The rotor of the generator is connected with the hull. The stator thereof is arranged to be anchored at a sea/lake bottom. According to an embodiment of the invention, the rotor is mounted in the cross direction by means of rolling elements. These are arranged between rolling surfaces on the rotor and support surfaces of a support means. The rolling elements are arranged to roll against the rolling surfaces and the support surfaces. The invention also relates to a wave power plant built up from wave power assemblies according to the invention. Furthermore, the invention relates to a use of the wave power assembly and a method for generating electric energy.