Wave structure interaction problems involve the understanding of the fluid phenomena which is in contact with the atmosphere and the behavior of the structure that is in contact with the fluid in addition to the phenomenon of wave propagation. This interdisciplinary branch embodies the basic equations of fluid mechanics, structural mechanics, concepts on wave propagation and the critically important role of some special types of boundary conditions. There is a parallel interest in analysing wave interaction with a large floating ice sheet which is also modeled as a large floating elastic plate and is of significant importance in the marginal ice zone of the polar region. In many situations, the structures are considered flexible in nature and hydroelastic analysis is made to analyse several hydrodynamic characteristics. Some of these structures have the advantages over the traditional rigid structure because they are reusable, environmental friendly and cost-effective. As a result, a substantial growth of knowledge in the dynamics of ocean surface waves and their effects on ocean structures has been witnessed in the past two decades.