The Present Work Mainly Deals With A Class Of Problems In The Broad Area Of Wave Structure Interaction Related To Hydroelasticity. In The Present Study, Major Emphasis Is Given • To Generalize The Mathematical Tools For A Class Of Physical Problems Associated With Laplace And/Or Helmholtz Type Equation Having Higher Order Boundary Conditions, • To Illustrate The Utility Of The Developed Mathematical Tools By Investigating A Class Of Physical Problems Which Are Of Recent Scientific Interest In The Broad Area Of Wave Structure Interaction Arising In Ocean And Arctic Engineering. In The Present Thesis, Generalized Expansion Formulae For The Wave Structure Interaction Problems Are Developed Based On The Application Of Fourier Analysis, Green’s Function Technique For Ordinary Differential Equation And Analytic Property Of The Complex Function Theory In Both The Cases Of A Semi-Infinite Strip And A Quarter Plane. Generalized Form Of The Orthogonal Mode-Coupling Relations Are Also Derived In Both The Cases Of A Semi-Infinite Strip And A Quarter Plane. As Applications Of The Expansion Formulae, Flexural Gravity Wave Scattering By Single And Multiple Articulated Floating Finite And Infinite Elastic Plates Are Analyzed Based On Small Amplitude Linearized Water Wave Theory. In The Case Of Multiple Articulated Floating Elastic Plates, The Solution For The Boundary Value Problem Is Analyzed By Using Eigenfunction Expansion Method And Wide-Spacing Approximation Method. Transformation Of Oblique Flexural Gravity Wave Due To Multiple Variations In Bottom Topography In The Presence Of Uniform Compressive Force Is Studied By Using The Method Of Wide-Spacing Approximation. Further, Using Shallow Water Approximation, The Flexural Gravity Wave Scattering Due To (I) Articulated Floating Elastic Plates And (Ii) Abrupt Changes In Bottom Topography Are Analyzed And The Explicit Relation For The Shoaling And Scattering Coefficients Are Obtained. Finally, Surface Gravity Wave Scattering By Floating Membrane Of Semi-Infinite And Finite Length Due To Change In Bottom Topography Are Analyzed. The Energy Relation Associated With Transformations Of Flexural Gravity Waves And Floating Membrane Are Derived Based On The Law Of Conservation Of Energy Flux And Also By The Direct Application Of Green’s Identity. The Numerical Results For The Reflection And Transmission Coefficients, Plate/Membrane Deflection, Phase And Group Velocity Are Computed In Different Cases And Analyzed. Keywords: Fourier Analysis; Regularity Criteria; Orthogonal Mode-Coupling Relation; Linearized Small Amplitude Wave Theory; Flexural Gravity Waves; Shallow Water Approximation; Multiple Articulation; Wide-Spacing Approximation; Energy Relation. Xiii