The main objective of this study is to perform the free and forced vibration analysis of transversely isotropic and laminated composite parabolic arches with a continuous cross-section variation. The anisotropy of the material of the arch, effects of the rotary inertia, and shear deformations are considered. An efficient unified numerical procedure of the Complementary Functions Method and Laplace transform is applied to solve the strong form of the differential equations that govern the dynamic response of the above structures. The validity and the accuracy of the presented scheme are tested by means of several comparisons with available literature and results of ANSYS. The presented approach has proven to be an accurate and stable numerical method. It is believed that derived results can be used as benchmark solutions for validation of related works in the future.