Under the assumptions of the linearised theory of small-amplitude water waves, it is proved that plane waves normally-incident upon a semi-immersed cylinder of uniform circular cross-section floating freely on the surface of a fluid of infinite depth are capable of being totally reflected. Numerically this is shown to occur at a single non-dimensional frequency. This remarkable result is used to construct examples of motion trapped modes, involving pairs of freely-floating cylinders moving either in phase or out of phase. The former case is equivalent to having a motion trapped mode for a single such cylinder next to a rigid vertical wall. In the latter out-of-phase case, the pair of cylinders move as if they form the wetted sections of a single rigidly-connected catamaran structure.