Linear problems of hydroelastic wave d iffraction by structures with vertical walls are s tudied for a circular cylinder frozen in ice cover of constant thickness and infinite extent. The wa ter depth is constant. The ice plate is modelled b y a thin elastic plate clamped to the surface of t he cylinder. The cylinder is mounted at the sea bo ttom. One-dimensional incident hydroelastic wave o f small amplitude propagates towards the cylinder and is diffracted on the cylinder. \; Deflecti on of the ice plate and the bending stresses in it are determined by two methods: (a) using the inte gral Weber transform in radial direction\, (b) usi ng the vertical modes for the fluid of constant de pth with the rigid bottom and elastic upper bounda ry. The solution by the second method is straightf orward but we cannot prove that the solution is co mplete because the properties of the vertical mode s are not known. \; The solution by the Weber transform is more complicated but this solution is unique. We will show that these two solutions are identical. This result justifies the method of th e vertical modes in the hydroelastic wave diffract ion problems. For a circular cylinder the vertical -mode solution can be also justified by substituti on. Different conditions at the contact line betwe en the cylinder and the ice sheet are considered. The wave diffraction problem for broken ice is als o considered. It is shown how the problem can be g eneralised to non-circular cylinders and interacti on of several cylinders in ice. LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR