The general trend in the aerospace industry is to optimise lightweight and highly flexible wing structures made of composite materials. This flexibility gives rise to static and dynamic aeroelastic instability problems. Research by Kim and Lee, Murua et al., and Drazumeric et al. have proven that chord-wise flexibility has a significant effect on the aeroelastic characteristics of an airfoil [1–3]; including the aeroelastic instability boundaries. Drazumeric et al. have numerically and experimentally shown that by adding chord-wise flexibility the stability boundaries could be increased up to 79.2% in the region of bimodal flutter behaviour, meaning that conventional section flutter and plate flutter occur simultaneously. It has been identified that the two-dimensional aeroelastic characteristics of flexible airfoil has been studied for constant stiffness flexible airfoils only. The present project will take the next step by assuming a piecewise constant thickness distributed flexible trailing edge. An elastically supported rigid airfoil shaped leading edge with attached a flexible composite plate was considered. The piecewise constant thickness distribution of the flexible plate was optimized for increasing the critical flow velocity at which the aeroelastic instabilities occur. An aeroelastic model has been developed to determine the aeroelastic characteristics of an elastically supported airfoil with attached a flexible piecewise constant thickness distributed trailing edge. The thin airfoil is assumed to harmonically oscillate with small amplitudes. The aerodynamic forces and moments are calculated by adopting the Küssner and Schwarz model which relates the pressure distribution over the airfoil to the downwash [4]. The transverse motion of the plate is modelled as an Euler-Bernoulli beam under the assumption that no span-wise deformations in the flexible trailing edge occur. The aeroelastic stability boundary is obtained by solving a complex eigenvalue problem in matrix form. The solutions to the system of equations are obtained as couples of the reduced frequency with the corresponding critical flow speed. The aeroelastic model is used to tailor the thickness distribution of the flexible trailing edge to optimise for the critical flow speed. Optimisations are executed for airfoil sections with conventional sectional parameters and with unconventional sectional parameters. In all cases it can be seen that a convergence in critical flow velocities was obtained for a trailing edge divided in two sections with a constant thickness. Depending on the length of the flexible trailing edge an increase up to 76% was achieved for airfoils with unconventional parameters, while for airfoils with conventional parameters a limited increase up to 4.1% was achieved.