The Work Presented In This Thesis Reports The Free Vibration, Buckling And Dynamic Instability Behavior Of Five Different Shell Forms Made Up Of Laminated Composite And Functionally Graded Materials. The Shell Forms Investigated Are Singly Curved Cylindrical Shell Panels And Doubly Curved Spherical, Hyperbolic Paraboloid Shell Panels, Having Only Principal Curvatures And Hypar Shell Panel Having Only And Conoid Shell Panels Having Twist Curvature Also. An Available Higher-Order Shear Deformation Theory Is Extended By Including The Twist Radius Of Curvature. The Finite Element Model Developed In The Present Study Satisfies C0 Continuity. The Objective Of The Present Study Is To Perform Linear Static Analysis Of Laminated Composite And Free Vibration, Buckling And Dynamic Instability Analyses Of Laminated Composite And Functionally Graded Shell Panels Employing Higher-Order Shear Deformation Theory. The Properties Of Functionally Graded Materials Are Considered To Be Both Temperature Dependent And Temperature Independent. A Generalized Finite Element Formulation Having All Three Radii Of Curvature For Analyzing Five Different Shell Forms Is Developed. The Appropriate Mesh Sizes Are Determined By Carrying Out Convergence Studies And The Correctness Of The Formulation Is Established By Taking Up Comparison Studies. The Regions Of Dynamic Instability Are Determined Following The Bolotin’s Procedure. Results Are Presented For Three Different Boundary Conditions (Simply Supported, Clamped And Corner Supported). Investigations Are Carried Out To Study The Effects Of Different Geometrical Parameters And Material Properties On The Free Vibration, Buckling And Dynamic Instability Characteristics Of Different Shell Forms.