An accommodating intraocular lens, for use in an eye, is made from flexible, bio-compatible lens body material surrounding a closed and sealed lens cavity which is filled with bio-compatible optical liquid. The optical liquid has a refractive index sufficiently high to, in cooperation with the ciliary muscle and accommodation of the lens body. focus light, incident on the eye, on the retina, and thus to provide accommodation. Connecting structure of the lens is interfaced with the ciliary muscle of the eve. The pressure expressed by the ciliary muscle, during the accommodative effort, is received by the connecting structure as a pushing force, and is transferred, as a pushing force, to the lens body, thus to change the radius of curvature of the anterior body member and/or the posterior body member, thus providing smooth focusing, including from far distance in the relaxed state to near distance in the accommodative state.