We present transmission and phase measurements on a birefringent YAlO(3) crystal that is illuminated with linearly polarized terahertz radiation in a broad frequency range (10 cm(-1) to 16 cm(-1)). The spectra exhibit pronounced and complex Fabry-Perot resonances that depend on the polarization orientation of the incoming light. We present a theoretical description to analyze these data and to obtain the optical constants of the crystal in the terahertz range.