This paper is concerned with the polarization states of an inhomogenously refracted P-wave induced from the interface of two anisotropic rocks. Two realistic physical models have been studied: Model-1 is an interface between anisotropic shale and Taylor sandstone; Model-2 is an interface between anisotropic shale and oil shale. For each model, an analytical expression of the polarization states was derived and its elliptical-polarization trajectory was examined. It is shown that an anomalous incident-angle leads not only to a sudden elliptical-polarization directional variation but also to an abrupt change in size and shape of its elliptical-polarization trajectory. The calculated results and analyses provide a theoretical base for the understandings of an anomalous incident-angle recently reported in the literature [e.g., Fa, Fa, Zhang, Ding, Gong, Li, Li, Tang, and Zhao (2015). Sci. Rep. 5, 12700].