In this article, the in-plane forced vibration behavior of transversely isotropic and laminated composite parabolic arches is examined by the unified scheme of the complementary functions method (CFM) and the Laplace transform theoretically. The anisotropy of the material of the arch, and the effects of the axial deformation, rotary inertia, and shear deformation are taken into account in the related assumptions and formulations. The arch is assumed to be made of anisotropic, linear elastic, and homogeneous material. For the solution of the governing equations, the RK5 (5th-order Runge-Kutta) algorithm has been used and for this aim, a software is written in FORTRAN. To transfer the obtained results back to the time space, an appropriate inverse method is used. Numerical results are presented and compared with solutions of ANSYS. As a result, the presented method is proved to be accurate and more efficient than the time integration methods.