In this study the computer programs for transonic flutter analysis have been developed which can be applied to two-dimensional airfoils and three-dimensional wings. Using the developed Euler codes, the transonic flutter analyses have been performed for two-dimensional typical section model with a flap degree-of-freedom and three- dimensional isotropic and composite wings. Time dependant compressible Euler equations, which are used to calculate steady and unsteady aerodynamics and generalized aerodynamic forces, are solved using a central-differenced finite volume scheme and two kinds of time integration methods(4th order Runge-Kutta method and diagonalized alternating direction implicit method). The dynamic grid generation procedure which is applied to generate instantaneous grid of a moving body at every time step during unsteady motion is carried out using the spring analogy method and the linear interpolation method. The transient pulse technique has been introduced to obtain generailzed aerodynamic forces which are necessary to calculate flutter points by the U-g method. The composite wing structures are modeled as a laminated composite plate. The generalized mass and stiffness matrices are generated using the finite element method based on the first-order shear deformable theory. The surface spline method is employed to interconnect the structural nodal and aerodynamic grid points. The flutter boundary is predicted using both the coupled time-integration method and the U-g method. To validate the developed flutter analysis codes, many numerical examinations have been performed for steady and unsteady aerodynamics, generalized aerodynamics, and flutter results. The present results have been compared with experimental and other numerical results and are proved to have a good agreement with the previous results. The present codes have been applied to the two- dimensional typical section model with a flap degree-of-freedom and three-dimensional isotropic and composite wings. In case of the flap degree-of-freedom typical section model, the instability of the flap motion increases as Mach number and the initial flap angle increase and/or the structural damping coefficient decreases. In case of the three dimensional isotropic wing, which is a rectangular wing with a biconvex airfoil, the computed flutter dynamic pressures are very accurate compared with experiment and the DLM results. As the airfoil thickness of the wing(the strength of steady shock wave) increases, the flutter dynamic pressure increases both in the transonic and sub- supersonic flow regime. In case of the composite wing, the characteristics of flutter boundary in the transonic flow region are very different from those in subsonic flow regime because of aerodynamic nonlinearities.