The travel time curve of reflection waves may not be hyperbolic, and the reflection point may not be located at the midpoint between the source and receiver for P-waves reflected from the bottom of a horizontal anisotropic layer. In this study, we used a physical model and numerical calculations to study travel times and reflection points for P-waves reflected from transversely isotropic media. We show that the reflection normal moveout (NMO) of the P-waves reflected from the bottom of a horizontal transversely isotropic (TI) layer is hyperbolic within the intermediate offset. The reflection points in the common midpoint (CMP) gather are located at the CMP of the P-waves reflected from TI strata with vertical (VTI) and horizontal (HTI) symmetry axes. However, the reflection points deviate from the CMP for media where the dip angles of the symmetry axes are not vertical and horizontal. The amount of deviation of the reflection points from the CMP depends not only on the offset but also on the dip angle, and the deviations are visualized by physical modeling. Thus, we must be extremely cautious about using the common depth point (CDP) shooting technique and NMO velocity to process seismic data reflected from anisotropic media.