The periodic response of cross-ply composite curved beams subjected to harmonic excitation with frequency in the neighborhood of symmetric and antisymmetric linear free vibration modes is investigated. The analysis is carried out using higher-order shear deformation theory based finite element method (FEM). The governing equations are integrated using Newmark’s time marching coupled with shooting technique and arc-length continuation. Shooting method is used to solve the second-order differential equations of motion directly without converting them to the first-order differential equations. This approach is computationally efficient as the banded nature of equations is retained. A detailed study revealed that the response of antisymmetrically excited beams has contribution of higher antisymmetric as well as symmetric modes whereas the response of symmetrically excited beams has the significant participation of the higher symmetric modes except for the excitation in the neighborhood of first symmetric mode. The beam excited in the neighborhood of first symmetric mode has an additional branch corresponding to significant participation of first antisymmetric mode due to two-to-one internal resonance. Furthermore, for the beams excited in the neighborhood of higher modes, the peak response amplitude becomes less than that of the beam excited in the neighborhood of first mode but vibration behavior is drastically different due to the presence of subharmonics and higher harmonics. Two-to-one internal resonance between second antisymmetric mode and first symmetric mode is predicted for the first time.