In the terahertz spectroscopy experiment, the tested solid samples surface is usually parallel and smooth to improve the systems signal-to-noise ratio. However, the objects surface in its natural state may show particular morphology such as depression and bulge, which will affect the terahertz spectrum in practical applications such as security inspection. These effects are related to the size of the particular morphology, but the most easily overlooked is that these effects are also related to the spatial distribution of terahertz waves. In this paper, firstly, we establish a model according to the terahertz transmission process of concave surface samples based on Gaussian optics. The influence of the regular cylinderconcave surface on the terahertz transmission spectra is studied. The Gaussian optical parameters of the terahertz spectrum system are measured by the small-aperture fitting method, and the parameters such as the beam waist radius of the terahertz wave are obtained. Then, polytetrafluoroethylene with a regular cylinderconcave surface is selected as the experiment material. The theoretical model value of transfer function amplitude is compared with the experiment value to verify the models applicability. The necessity of taking a terahertz wave as the Gaussian beam when there are defects such as a concave surface is confirmed through the experiment. Finally, it is inferred from the model that the quantitative effects of depression depth and depression radius on terahertz transmission spectra, in the directions parallel and perpendicular to the propagation direction of terahertz wave: with the increase of depression depth, the spectral transfer function amplitude period becomes smaller and smaller. It is a monotonous quantitative relationship that will not be affected by the depression radius. The quantitative detection of depression depth can be realized using this quantitative relationship between depression depth and the spectral transfer function amplitude period. When the available spectra width is 1.2 THz, the minimum detection limit of depression depth is 0.53 mm; With the increase of depression radius, the average spectral transfer function amplitude decreases first and then increases. There is no monotonic function relationship between them, which is affected by depression depth. When the depression radius is greater than 5 mm, the mean value of the spectral transfer function amplitude no longer increases with the increase of the radius. The influence of the depression on the spectral transfer function amplitude is also related to the depression position. These two phenomena are mainly related to the Gaussian distribution of the terahertz waves. The conclusions of this study can be used in the nondestructive testing of surface defects of nonpolar materials by terahertz wave. They can also be used to design the surface morphology of samples to make them have the desired spectral transfer function.