The primary objective of the current research is to develop a Computational Fluid Dynamics (CFD) model to investigate rigid and flexible aerofoil propulsive characteristics when the aerofoil IS subjected to oscillatory flapping motions. The study is also extended to rectangular wings. Flows past the flapping aero foils at moderate Reynolds numbers are simulated using the twodimensional incompressible Navier-Stokes equations. The Baldwin-Lomax algebraic turbulence model is incorporated to determine eddy viscosity for higher Reynolds numbers turbulent flow simulations. Flows past flapping wings are simulated using strip theory, which computes the flows in multiple two-dimensional planes located at intervals along the wing span. The flows are assumed locally. two-dimensional and the three-dimensional effects between each section are incorporated via the consideration of vortex lattice effects. The simulations are modelled using piecewise linear finite element approximation method on an unstructured triangular finite element mesh. A dynamic moving mesh is used to compute flexible aerofoils and wings. The mesh is remeshed at each fluid time step using the spring segment analogy method. A novel treatment of the near.-wall viscous grids ensures that the good orthogonal properties are maintained to facilitate the turbulence computations. A wide range of simulations is carried out for an oscillatory heaving NACA0012 aerofoil. Parametric studies of basic parameters like the amplitude of oscillation, its reduced frequency, and the flow freestream Reynolds numbers effects on aero foil performance are conducted. The influences of the flexural profile on the flexible aerofoil propulsive characteristics are also investigated. The rectangular wing, oflow aspect ratio 4 and NACA0012 aerofoil cross-sections, is also simulated in oscillatory heaving motion. The chordwise flexural effects of the heaving flexible wing on its propulsive characteristics are studied too.