We study the effects of having an opening in a vertical cylinder of an arbitrary cross-sectional shape when subjected to incident waves from the outside field. Both the diffraction and radiation problems of linear potential-flow theory are addressed. The cylinders considered are bottom-mounted with vanishing thickness and the problem is formulated as a hypersingular boundary-integral method. A simple higher-order procedure is presented to handle the strong singularity. Comparisons are made between the hydrodynamic properties of open and closed cylinders, and the effects of increasing the opening size are discussed and explained. Results for square, circular and elliptical open cylindrical shells, presented as examples, indicate that wave loads on the structures could be dramatically decreased to zero (effectively) at certain frequencies and opening sizes. This leads to the surprising conclusion that directing an open structure into the incident-wave field results in lower loads on the structure. A model of an open harbour with a frontal breakwater in a wave field, inspired by the idea of the Portunus Project, is also analysed.