The purpose of the work presented in the paper, is to compute the response of transversely isotropic plane layered media excited by a buried or surface source, in order to obtain a method which can help interpreting real seismograms. The computation in frequency f and wavenumber k domain based on the Kennett＇s reflectivity method is exposed. Displacements in space and time are calculated by numerical integration (Fourier-Hankel transform) of the response in frequency and wavenumber domain. The numerical surface response of a transverse isotropic two-layered half space excited by a surface source is presented. The mechanical properties of the proposed two-layered halfspace falls within the range of marine sediments. The frequency and offset proposed domain correspond with geotechnical surveys. Effects of anisotropy are put forward by comparing the responses in anisotropic case to the responses in isotropic case.