Abstract: This study examines the interaction between a rigid circular plate and a transversely isotropic layered half-space. The transversely isotropic layered half-space consists of finite layers and a lower half-space. The dissimilar layers are homogeneous and fully bonded. Each layer can be either transversely isotropic or isotropic. The rigid circular plate is smoothly placed on the horizontal boundary surface of the transversely isotropic layered half-space and subjected to a moment about a horizontal axis. Classical integral transform methods are used to solve the mixed boundary value problem. In the transform domain, the Fredholm integral equation of the second kind is established to describe the interaction between the rigid plate and the transversely isotropic layered half-space. A closed-form solution is derived for the elastic field of a transversely isotropic layered half-space subjected to indentation by a rigid circular plate. An isolating technique is employed to address the weak convergence of the integral associated with the kernel functions, and corresponding numerical methods are developed to solve the closed-form solution of this contact problem. Finally, the numerical results illustrate the influence of non-homogeneity and transverse isotropy on the elastic fields of layered half-spaces. The methods proposed are suitable for any type of transversely isotropic layered half-space with an arbitrary number of layers.